If f(x) = 3^x and g(x) = 2x + 5, at which value, №18010296, 11.07.2021 22:04

Mathematics

If f(x) = 3^x and g(x) = 2x + 5, at which value of x is f(x) g(x)? A. -1 B. 2 C. -3 D. -4

Step-by-step answer

P Answered by Master

A) x = -1

Step-by-step explanation:

$f(-1)=3^{-1}=\dfrac13\\\\g(-1)=2(-1)+5=3\\\\\implies f(x) < g(x)$

$f(2)=3^{2}=9\\\\g(2)=2(2)+5=9\\\\\implies f(x)=g(x)$

$f(-3)=3^{-3}=\dfrac{1}{27}\\\\g(-3)=2(-3)+5=-1\\\\\implies f(x) g(x)$

$f(-4)=3^{-4}=\dfrac{1}{81}\\\\g(-4)=2(-4)+5=-3\\\\\implies f(x) g(x)$

Mathematics

Integrated Mann ist Quarter) English Given f(x) = 3x-1 and g(x) = 2x-3, for which value of x does slx) = f(2)? 3 PRO X-2 5 O X= 2 O x=4

Step-by-step answer

P Answered by PhD

2

g(x)=f(2) for x = 4

Step-by-step explanation:

If f(x)=3x-1

and g(x)= 2x-3

Then for which value of "x" does g(x)=f(2) ?

So start by evaluating what f(2) is:

$f(x)=3x-1\,\,\,\,therefore\,\,\,\, f92)=3\,(2)-1=6-1=5$

Then,we have to find for which value of x g(x)=5

so we write g(x) explicitly:

$2x-3=5\\2x=5+3\\2 x = 8\\x = 8/2\\x=4$

Mathematics

Given f(x) = 3x-1 and g(x)=2x-3, for which value of x does g(x)=f(2)? Ox=3/2 Ox-2 Ox=5/2 Ox=4

Step-by-step answer

P Answered by PhD

31

x = 4

Work Shown:

First find f(2)

f(x) = 3x-1

f(2) = 3(2)-1 ... replace every x with 2

f(2) = 6-1

f(2) = 5

The equation g(x) = f(2) is the same as g(x) = 5 since f(2) = 5

g(x) = 2x-3

5 = 2x-3 replace g(x) with 5

2x-3 = 5

2x = 5+3 ... add 3 to both sides

2x = 8

x = 8/2 divide both sides by 2

x = 4

Mathematics

Integrated Mann ist Quarter) English Given f(x) = 3x-1 and g(x) = 2x-3, for which value of x does slx) = f(2)? 3 PRO X-2 5 O X= 2 O x=4

Step-by-step answer

P Answered by PhD

2

g(x)=f(2) for x = 4

Step-by-step explanation:

If f(x)=3x-1

and g(x)= 2x-3

Then for which value of "x" does g(x)=f(2) ?

So start by evaluating what f(2) is:

$f(x)=3x-1\,\,\,\,therefore\,\,\,\, f92)=3\,(2)-1=6-1=5$

Then,we have to find for which value of x g(x)=5

so we write g(x) explicitly:

$2x-3=5\\2x=5+3\\2 x = 8\\x = 8/2\\x=4$

Mathematics

Compare the functions below f(x)=3^x+2 g(x)=20x+4 h(x)=2x^2+5x+2 select the true statements 1. over the interval [2,3], the average rate of change of g is lower than that of both f and h 2. as x increases on the interval [0,infinity), the rate of change of g eventually exceeds the rate of change of both f and h 3. when x = 4, the value of f(x) exceeds the values of both g(x) and h(x) 4. when x=8, the value of h(x) exceeds the values of both f(x) and g(x) 5 as x increases on the interval [0,infinity), the rate of change of f eventually exceeds the

Step-by-step answer

P Answered by Master

9

Step-by-step explanation:

Given are three functions, f, g and h. We are to check the validity of the statements from 1 to 5

1) Avg rate of change of functions in the interval [2,3]

f(x) = f(3)-f(2) =29-11=18

g(x) = g(3)-g(2) =64-44=20

h(x) = h(3)-h(2) = 15

False

2) False, From the graph given we find that it is false

3) True since f(4) is higher than other function value at 4.

4) h(8) = 128+40+2 =170. f(8) = 6563

Hence false.

5) f'(x) =3^x lnx: g'(x) = 20: h'(x) = 4x+5

False because when x=1, rate of change of f = 0<g'(x)

Last statement a quantity increasing exponentially eventually exceeds a quantity growing quadratically or linearly

is true

Mathematics

Compare the functions below f(x)=3^x+2 g(x)=20x+4 h(x)=2x^2+5x+2 select the true statements 1. over the interval [2,3], the average rate of change of g is lower than that of both f and h 2. as x increases on the interval [0,infinity), the rate of change of g eventually exceeds the rate of change of both f and h 3. when x = 4, the value of f(x) exceeds the values of both g(x) and h(x) 4. when x=8, the value of h(x) exceeds the values of both f(x) and g(x) 5 as x increases on the interval [0,infinity), the rate of change of f eventually exceeds the

Step-by-step answer

P Answered by Specialist

9

Step-by-step explanation:

Given are three functions, f, g and h. We are to check the validity of the statements from 1 to 5

1) Avg rate of change of functions in the interval [2,3]

f(x) = f(3)-f(2) =29-11=18

g(x) = g(3)-g(2) =64-44=20

h(x) = h(3)-h(2) = 15

False

2) False, From the graph given we find that it is false

3) True since f(4) is higher than other function value at 4.

4) h(8) = 128+40+2 =170. f(8) = 6563

Hence false.

5) f'(x) =3^x lnx: g'(x) = 20: h'(x) = 4x+5

False because when x=1, rate of change of f = 0<g'(x)

Last statement a quantity increasing exponentially eventually exceeds a quantity growing quadratically or linearly

is true

Mathematics

A coordinate grid with 2 lines. The first line is labeled f(x) and passes through (negative 4, 3), (0, 3) and (4, 3). The second line is labeled g(x) and passes through the points (negative 2, negative 5), (0, negative 2), and (2, 1) Determine the input value for which the statement f(x) = g(x) is true. From the graph, the input value is approximately (2) (2.5) (3.5) or (4) . f(x) = 3 and g(x) = 3/2x – 2 3 = 3/2x – 2 5 = 3/2x The x-value at which the two functions’ values are equal is (2/3) (3/2) (5/3) or (10/3) .

Step-by-step answer

P Answered by Master

20

3.5 and 10/3

Step-by-step explanation:

just took the quiz

Mathematics

A coordinate grid with 2 lines. The first line is labeled f(x) and passes through (negative 4, 3), (0, 3) and (4, 3). The second line is labeled g(x) and passes through the points (negative 2, negative 5), (0, negative 2), and (2, 1) Determine the input value for which the statement f(x) = g(x) is true. From the graph, the input value is approximately (2) (2.5) (3.5) or (4) . f(x) = 3 and g(x) = 3/2x – 2 3 = 3/2x – 2 5 = 3/2x The x-value at which the two functions’ values are equal is (2/3) (3/2) (5/3) or (10/3) .

Step-by-step answer

P Answered by Master

20

3.5 and 10/3

Step-by-step explanation:

just took the quiz

Mathematics

7 QUESTIONS: Function f is nonlinear and f(5)=4. Which equation could represent function f? a. f(x)=x^2-11 b. f(x)=2^x-28 c. f(x)=5 d. f(x)=1/5x+3 Which statement about function g is true? 1 10 2 40 3 160 4 640 a. function g is linear because the rate of change is constant. b. function g is exponential because the rate of change is constant. c. function g is exponential because g(x) changes by equal factors over equal intervals of x. d. function g is linear because g(x) changes by equal factors over equal intervals of x. Which statement describes

Step-by-step answer

P Answered by PhD

1) d. f(x)=1/5x+3.
2) a. function g is linear because the rate of change is constant.
3) d. as x approaches positive infinity, f(x) approaches negative infinity.
4) c. (-infinity, infinity).
5) d. (9,-3)
6) c. h(x)=12^2+12x-45

Mathematics

Given the functions: f(x) = 4x + 8 and g(x) = 2x − 3. Make a table of values for each function to determine which value of x is closest to where g(x) begins to exceed f(x). A) x = 4 B) x = 5 C) x = 6 D) x = 7

Step-by-step answer

P Answered by Master

6

Your answer is B

B) x+5

Step-by-step explanation:

x = 5

f(x) = 4x + 8 = 4(5) + 8 = 28

g(x) = 2x − 3 = 25 − 3 = 29

A quantity increasing exponentially eventually exceeds a quantity increasing linearly.

If f(x) = 3^x and g(x) = 2x + 5, at which value of x is f(x) < g(x)? A. -1
B. 2
C. -3
D. -4

Step-by-step answer

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If f(x) = 3^x and g(x) = 2x + 5, at which value of x is f(x) < g(x)? A. -1 B. 2 C. -3 D. -4

Step-by-step answer

Faq

Try asking the Studen AI a question.

If f(x) = 3^x and g(x) = 2x + 5, at which value of x is f(x) < g(x)? A. -1
B. 2
C. -3
D. -4