Given f(x)=3x+1, solve for x when f(x)=7., №9881451, 22.01.2022 19:39

Mathematics

Given f(x)=3x-1, solve for x when f(x)=-7.

Step-by-step answer

P Answered by PhD

4

x = -2

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Equality Properties

Algebra I

Function Notation

Step-by-step explanation:

Step 1: Define

f(x) = 3x - 1

f(x) = -7

Step 2: Solve for x

Substitute: -7 = 3x - 1Isolate x term: -6 = 3xIsolate x: -2 = xRewrite: x = -2

Mathematics

Given f(x)=3x+1, solve for x when f(x)=7

Step-by-step answer

P Answered by Master

${ \tt{f(x) = 3x + 1}}$

• when f(x) is 7,

${ \tt{3x + 1 = 7}} \\ \\ { \tt{3x = 6}} \\ \\ { \tt{x = \frac{6}{3} }} \\ \\ { \boxed{ \rm{ \: x = 2 \: }}}$

Mathematics

Given f(x)=3x-1, solve for x when f(x)=-7.

Step-by-step answer

P Answered by PhD

4

x = -2

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Equality Properties

Algebra I

Function Notation

Step-by-step explanation:

Step 1: Define

f(x) = 3x - 1

f(x) = -7

Step 2: Solve for x

Substitute: -7 = 3x - 1Isolate x term: -6 = 3xIsolate x: -2 = xRewrite: x = -2

Mathematics

Given f(x) = 3x + 1, solve for x when f(x) = 7.

Step-by-step answer

P Answered by PhD

f(7) = 22

Step-by-step explanation:

1. f(x) = 3x + 1

2. f(7) = 3(7) + 1

3. f(7) = 21 + 1

Mathematics

Given f(x) = 3x + 1, solve for x when f(x) = 7.

Step-by-step answer

P Answered by PhD

11

x = 2

Step-by-step explanation:

Step 1: Define

f(x) = 3x + 1

f(x) = 7

Step 2: Substitute

7 = 3x + 1

Step 3: Solve for x

6 = 3x

x = 2

Mathematics

Test due 12/1 the function f(x) = x − 1 is changed to f(x) = 1 4 x − 1. which describes the effect of the change on the graph of the original function? a) the line will be steeper. b) the line will be less steep. c) line changes from increasing to decreasing. d) line changes from decreasing to increasing. 2) sketch the linear function f(x) = 1 6 (3x + 1). which key feature of the graph is true? a) y-intercept (0, 1) b) x-intercept ( 1 6 , 0) c) x-intercept (− 1 3 , 0) d) y-intercept (0, − 1 6 ) 3) the graph of the line y = 4 is a a) vertical line

Step-by-step answer

P Answered by Master

1

1. f(x) = 1/4x − 1. B)The line will be less steep. The slope is lower now

2. C)x-intercept (−1/3 , 0). Replacing f(x) = 0 we get x = -1/3

3. B)horizontal line with a slope of zero. The slope is 0 because there is no x in the equation.

4. D)Line changes from decreasing to increasing. The slope changed from negative to positive.

5. See first graph attached

6. See second graph attached. g(x) = (1/3)*x

7. C)The rate of change is different, but the y-intercepts are the same. The rate of change of Mike is negative because he withdraws $25 each week. The y-intercepts of Mike is $200 because that was his initial deposit.

8. B)shifts the line 7 units down. f(x-7) translates f(x) 7 units to the right, given the slope is positive ( = 1) then f(x) is translated 7 units down.

9. No graph is shown

10. C)g(x) = x - 3. g(x) = f(x) - 3, so g(x) is f(x) translated 3 units down.

Test due 12/1 the function f(x) = x − 1 is changed to f(x) = 1 4 x − 1. which describes the effect o

Mathematics

Test due 12/1 the function f(x) = x − 1 is changed to f(x) = 1 4 x − 1. which describes the effect of the change on the graph of the original function? a) the line will be steeper. b) the line will be less steep. c) line changes from increasing to decreasing. d) line changes from decreasing to increasing. 2) sketch the linear function f(x) = 1 6 (3x + 1). which key feature of the graph is true? a) y-intercept (0, 1) b) x-intercept ( 1 6 , 0) c) x-intercept (− 1 3 , 0) d) y-intercept (0, − 1 6 ) 3) the graph of the line y = 4 is a a) vertical line

Step-by-step answer

P Answered by Specialist

1

1. f(x) = 1/4x − 1. B)The line will be less steep. The slope is lower now

2. C)x-intercept (−1/3 , 0). Replacing f(x) = 0 we get x = -1/3

3. B)horizontal line with a slope of zero. The slope is 0 because there is no x in the equation.

4. D)Line changes from decreasing to increasing. The slope changed from negative to positive.

5. See first graph attached

6. See second graph attached. g(x) = (1/3)*x

7. C)The rate of change is different, but the y-intercepts are the same. The rate of change of Mike is negative because he withdraws $25 each week. The y-intercepts of Mike is $200 because that was his initial deposit.

8. B)shifts the line 7 units down. f(x-7) translates f(x) 7 units to the right, given the slope is positive ( = 1) then f(x) is translated 7 units down.

9. No graph is shown

10. C)g(x) = x - 3. g(x) = f(x) - 3, so g(x) is f(x) translated 3 units down.

Mathematics

#1. given the binomials (x - 2), (x - 1), (x + 2), and (x - 4), which one is a factor of f(x) = x3 + 7x2 + 14x + 8? (x - 2) (x - 1) (x + 2) (x - 4) given the binomials (x + 1), (x + 4), (x - 5), and (x - 2), which one is a factor of f(x) = 3x3 - 12x2 - 4x - 55? (x + 1) (x + 4) (x - 5) (x - 2) #2. what is the f of x over the g of x when f(x) = 6x3 - 19x2 + 16x - 4 and g(x) = x - 2? 6x2 - 7x + 2/3x2 - 9x + 8/ 6x2 - 7x + 2 - 8 over the quantity of x minus 2/3x2 - 9x + 8 - 8 over the quantity of x minus 2 #3. what is the f of x over the g of x when

Step-by-step answer

P Answered by PhD

31

#1
Factoring the function:
f(x) = x3 + 7x2 + 14x + 8
f(x) = (x + 4) (x + 1) (x + 2)

From the options, (x + 2) is the factor

#2
f(x) / g(x) = (6x3 - 19x2 + 16x - 4) / (x - 2)
This can be solved by factoring the numerator, by synthetic division or using the remainder theorem.

The result is:
6x^2 - 7x + 2 or (x - 2/3)(x - 1/2)

#3 same with #2

#4
(x3 - 5x2 + 2x + 5) / (x - 2)
Again, this can be solved by a number of methods, the result is:
x2 -3x - 4 - (3/x-2)

Mathematics

#1. given the binomials (x - 2), (x - 1), (x + 2), and (x - 4), which one is a factor of f(x) = x3 + 7x2 + 14x + 8? (x - 2) (x - 1) (x + 2) (x - 4) given the binomials (x + 1), (x + 4), (x - 5), and (x - 2), which one is a factor of f(x) = 3x3 - 12x2 - 4x - 55? (x + 1) (x + 4) (x - 5) (x - 2) #2. what is the f of x over the g of x when f(x) = 6x3 - 19x2 + 16x - 4 and g(x) = x - 2? 6x2 - 7x + 2/3x2 - 9x + 8/ 6x2 - 7x + 2 - 8 over the quantity of x minus 2/3x2 - 9x + 8 - 8 over the quantity of x minus 2 #3. what is the f of x over the g of x when

Step-by-step answer

P Answered by PhD

31

#1
Factoring the function:
f(x) = x3 + 7x2 + 14x + 8
f(x) = (x + 4) (x + 1) (x + 2)

From the options, (x + 2) is the factor

#2
f(x) / g(x) = (6x3 - 19x2 + 16x - 4) / (x - 2)
This can be solved by factoring the numerator, by synthetic division or using the remainder theorem.

The result is:
6x^2 - 7x + 2 or (x - 2/3)(x - 1/2)

#3 same with #2

#4
(x3 - 5x2 + 2x + 5) / (x - 2)
Again, this can be solved by a number of methods, the result is:
x2 -3x - 4 - (3/x-2)

Mathematics

Good answers get brainliest. +40 points wrong answers get reported 9.05a 1. find the derivative of f(x) = 8x2 + 11x at x = 7. a) 123 b) -147 c) 156 d) 189 2. find the derivative of f(x) = 3x + 8 at x = 4. a) 1 b ) 3 c) 4 d) 8 3. find the derivative of f(x) = 5 divided by x at x = -1. a) 5 b) 1 c) -1 d) -5 4. find the derivative of f(x) = negative 7 divided by x at x = -3. a) 3 divided by 7 b) 9 divided by 7 c) 7 divided by 9 d) 7 divided by 3 5. find the limit of the function by using direct substitution. limit as x approaches zero of quantity

Step-by-step answer

P Answered by Master

1. Ans:(A) 123

Given function: f(x) = 8x^2 + 11x

The derivative would be:
$\frac{d}{dx} f(x) = \frac{d}{dx}(8x^2 + 11x)$
=> $\frac{d}{dx} f(x) = \frac{d}{dx}(8x^2) + \frac{d}{dx}(11x)$
=> $\frac{d}{dx} f(x) = 2*8(x^{2-1}) + 11$
=> $\frac{d}{dx} f(x) = 16x + 11$

Now at x = 7:
$\frac{d}{dx} f(7) = 16(7) + 11$

=> $\frac{d}{dx} f(7) = 123$

2. Ans:(B) 3

Given function: f(x) =3x + 8

The derivative would be:
$\frac{d}{dx} f(x) = \frac{d}{dx}(3x + 8)$
=> $\frac{d}{dx} f(x) = \frac{d}{dx}(3x) + \frac{d}{dx}(8)$
=> $\frac{d}{dx} f(x) = 3*1 + 0$
=> $\frac{d}{dx} f(x) = 3$

Now at x = 4:
$\frac{d}{dx} f(4) = 3$ (as constant)

=>Ans: $\frac{d}{dx} f(4) =$ 3

3. Ans:(D) -5

Given function: $f(x) = \frac{5}{x}$
The derivative would be:
$\frac{d}{dx} f(x) = \frac{d}{dx}(\frac{5}{x})$
or
$\frac{d}{dx} f(x) = \frac{d}{dx}(5x^{-1})$
=> $\frac{d}{dx} f(x) = 5*(-1)*(x^{-1-1})$
=> $\frac{d}{dx} f(x) = -5x^{-2}$

Now at x = -1:
$\frac{d}{dx} f(-1) = -5(-1)^{-2}$

=> $\frac{d}{dx} f(-1) = -5 *\frac{1}{(-1)^{2}}$
=> Ans: $\frac{d}{dx} f(-1) = -5$

4. Ans:(C) 7 divided by 9

Given function: $f(x) = \frac{-7}{x}$
The derivative would be:
$\frac{d}{dx} f(x) = \frac{d}{dx}(\frac{-7}{x})$
or
$\frac{d}{dx} f(x) = \frac{d}{dx}(-7x^{-1})$
=> $\frac{d}{dx} f(x) = -7*(-1)*(x^{-1-1})$
=> $\frac{d}{dx} f(x) = 7x^{-2}$

Now at x = -3:
$\frac{d}{dx} f(-3) = 7(-3)^{-2}$

=> $\frac{d}{dx} f(-3) = 7 *\frac{1}{(-3)^{2}}$
=> Ans: $\frac{d}{dx} f(-3) = \frac{7}{9}$

5. Ans:(C) -8

Given function:
f(x) = x^2 - 8

Now if we apply limit:
$\lim_{x \to 0} f(x) = \lim_{x \to 0} (x^2 - 8)$

=> $\lim_{x \to 0} f(x) = (0)^2 - 8$
=> Ans: $\lim_{x \to 0} f(x) = - 8$

6. Ans:(C) 9

Given function:
f(x) = x^2 + 3x - 1

Now if we apply limit:
$\lim_{x \to 2} f(x) = \lim_{x \to 2} (x^2 + 3x - 1)$

=> $\lim_{x \to 2} f(x) = (2)^2 + 3(2) - 1$
=> Ans: $\lim_{x \to 2} f(x) = 4 + 6 - 1 = 9$

7. Ans:(D) doesn't exist.

Given function: $f(x) = -6 + \frac{x}{x^4}$
In this case, even if we try to simplify it algebraically, there would ALWAYS be x power something (positive) in the denominator. And when we apply the limit approaches to 0, it would always be either + infinity or -infinity. Hence, Limit doesn't exist.

Check:
$f(x) = -6 + \frac{x}{x^4} \\ f(x) = -6 + \frac{1}{x^3} \\ f(x) = \frac{-6x^3 + 1}{x^3} \\ Rationalize: \\ f(x) = \frac{-6x^3 + 1}{x^3} * \frac{x^{-3}}{x^{-3}} \\ f(x) = \frac{-6x^{3-3} + x^{-3}}{x^0} \\ f(x) = -6 + \frac{1}{x^3} \\ Same$

If you apply the limit, answer would be infinity.

8. Ans:(A) Doesn't Exist.

Given function: $f(x) = 9 + \frac{x}{x^3}$
Same as Question 7
If we try to simplify it algebraically, there would ALWAYS be x power something (positive) in the denominator. And when we apply the limit approaches to 0, it would always be either + infinity or -infinity. Hence, Limit doesn't exist.

9, 10.
Please attach the graphs. I shall amend the answer. :)

11. Ans:(A) Doesn't exist.

First We need to find out: $\lim_{x \to 9} f(x)$ where,
$f(x) = \left \{ {{x+9, ~~~~~x \textless 9} \atop {9- x,~~~~~x \geq 9}} \right.$

If both sides are equal on applying limit then limit does exist.

Let check:
If x $\textless$ 9: answer would be 9+9 = 18
If x $\geq$ 9: answer would be 9-9 = 0

Since both are not equal, as $18 \neq 0$ , hence limit doesn't exist.

12. Ans:(B) Limit doesn't exist.

Find out: $\lim_{x \to 1} f(x)$ where,

$f(x) = \left \{ {{1-x, ~~~~~x \textless 1} \atop {x+7,~~~~~x \textgreater 1} } \right. \\ and \\ f(x) = 8, ~~~~~ x=1$

If all of above three are equal upon applying limit, then limit exists.

When x < 1 -> 1-1 = 0
When x = 1 -> 8
When x > 1 -> 7 + 1 = 8

ALL of the THREE must be equal. As they are not equal. 0 $\neq$ 8; hence, limit doesn't exist.

13. Ans:(D) -∞; x = 9

f(x) = 1/(x-9).

Table:

x f(x)=1/(x-9)

----------------------------------------

8.9 -10

8.99 -100

8.999 -1000

8.9999 -10000

9.0 -∞

Below the graph is attached! As you can see in the graph that at x=9, the curve approaches but NEVER exactly touches the x=9 line. Also the curve is in downward direction when you approach from the left. Hence, -∞, x =9 (correct)

14. Ans: -6

s(t) = -2 - 6t

Inst. velocity = $\frac{ds(t)}{dt}$

Therefore,

$\frac{ds(t)}{dt} = \frac{ds(t)}{dt}(-2-6t) \\ \frac{ds(t)}{dt} = 0 - 6 = -6$

At t=2,

Inst. velocity = -6

15. Ans: +∞, x =7

f(x) = 1/(x-7)^2.

Table:

x f(x)= 1/(x-7)^2

--------------------------

6.9 +100

6.99 +10000

6.999 +1000000

6.9999 +100000000

7.0 +∞

Below the graph is attached! As you can see in the graph that at x=7, the curve approaches but NEVER exactly touches the x=7 line. The curve is in upward direction if approached from left or right. Hence, +∞, x =7 (correct)

-i

Good answers get brainliest. +40 points wrong answers get reported 9.05a 1. find the derivative of f

Given f(x)=3x+1, solve for x when f(x)=7.

Faq

Try asking the Studen AI a question.