Chemistry : asked on ajbyrd911

17.07.2021

If f(x)=x^2 and g(x)=2x+3, what is f(g(x))

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09.07.2023, solved by verified expert

Mathematics, English, Physics. Research Scholar at Indian Institute of Technology, Roorkee

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Explanation:

In its raw form, function notation essentially represents an equation with only one unknown variable, expressed in terms of another. Thus, f(x) = x² + 7x can be expressed as

g(x) = 2x + 3

f(g(x)) = (2x + 3)²

f(g(x)) = 4x² + 12x + 9

Hope it helps :) and let me know if you want me to elaborate.

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Mathematics

Asap if f(x)= x^2 and g(x)= 2x+3, what is f (g( a. 4x^2+9 b. x^2+2x+3 c. 2x^2+3 d. 4x^2+12x+9

Step-by-step answer

P Answered by PhD

D

Step-by-step explanation:

Substitute x = g(x) into f(x)

f(2x + 3) = (2x + 3)² ← expand factors

f(g(x)) = (2x)² + 6x + 6x + 3² = 4x² + 12x + 9 → D

Mathematics

Asap if f(x)= x^2 and g(x)= 2x+3, what is f (g( a. 4x^2+9 b. x^2+2x+3 c. 2x^2+3 d. 4x^2+12x+9

Step-by-step answer

P Answered by PhD

D

Step-by-step explanation:

Substitute x = g(x) into f(x)

f(2x + 3) = (2x + 3)² ← expand factors

f(g(x)) = (2x)² + 6x + 6x + 3² = 4x² + 12x + 9 → D

Chemistry

If f(x)=x^2 and g(x)=2x+3, what is f(g(x))

Step-by-step answer

P Answered by Specialist

$\huge\boxed{f(g(x)) = 4x^2 + 12x + 9}$

Explanation:

In its raw form, function notation essentially represents an equation with only one unknown variable, expressed in terms of another. Thus, f(x) = x² + 7x can be expressed as

g(x) = 2x + 3

f(g(x)) = (2x + 3)²

f(g(x)) = 4x² + 12x + 9

Hope it helps :) and let me know if you want me to elaborate.

Mathematics

For f(x)=x+2 and g(x)=2x+3, find the following functions. a. (f◦g)(x); b. (g◦f)(x); c. (f◦g)(0); d.

Step-by-step answer

P Answered by PhD

Here you go!! Hope this helps
For f(x)=x+2 and g(x)=2x+3, find the following functions. a. (f◦g)(x); b. (g◦f)(x); c. (f◦g)(0); d.

For f(x)=x+2 and g(x)=2x+3, find the following functions. a. (f◦g)(x); b. (g◦f)(x); c. (f◦g)(0); d.

Mathematics

Let f(x) = x^2 and g(x) = 2x + 3. write an expression that represents each composition: a. (g ∘ f)(x) b. f(f(−2)) c. (f ∘ g) (1 / x)

Step-by-step answer

P Answered by Master

Remember, if f and g are functions then $(f\circ g)(x)=f(g(x))$ , then:

a) $(g\circ f)(x)=g(f(x)))=g(x^2)=2(x^2)+3=2x^2+3$

b) f(f(-2))=f((-2)^2)=f(4)=4^2=16

c)

$(f \circ g)(\frac{1}{x})=f(g(\frac{1}{x}))\\=f(2(\frac{1}{x})+3)\\=f(\frac{2}{x}+3)\\=(\frac{2}{x}+3)^2\\ =(\frac{2}{x})^2+2*\frac{2}{x}*3+3^2 \\ =\frac{4}{x^2}+\frac{12}{x}+9$

then, $(f\circ g)=\frac{4}{x^2}+\frac{12}{x}+9$

Mathematics

For f(x)=x+2 and g(x)=2x+3, find the following functions. a. (f◦g)(x); b. (g◦f)(x); c. (f◦g)(0); d.

Step-by-step answer

P Answered by PhD

Here you go!! Hope this helps
For f(x)=x+2 and g(x)=2x+3, find the following functions. a. (f◦g)(x); b. (g◦f)(x); c. (f◦g)(0); d.

For f(x)=x+2 and g(x)=2x+3, find the following functions. a. (f◦g)(x); b. (g◦f)(x); c. (f◦g)(0); d.

Mathematics

Let f(x) = x^2 and g(x) = 2x + 3. write an expression that represents each composition: a. (g ∘ f)(x) b. f(f(−2)) c. (f ∘ g) (1 / x)

Step-by-step answer

P Answered by Specialist

Remember, if f and g are functions then $(f\circ g)(x)=f(g(x))$ , then:

a) $(g\circ f)(x)=g(f(x)))=g(x^2)=2(x^2)+3=2x^2+3$

b) f(f(-2))=f((-2)^2)=f(4)=4^2=16

c)

$(f \circ g)(\frac{1}{x})=f(g(\frac{1}{x}))\\=f(2(\frac{1}{x})+3)\\=f(\frac{2}{x}+3)\\=(\frac{2}{x}+3)^2\\ =(\frac{2}{x})^2+2*\frac{2}{x}*3+3^2 \\ =\frac{4}{x^2}+\frac{12}{x}+9$

then, $(f\circ g)=\frac{4}{x^2}+\frac{12}{x}+9$

Mathematics

Me. 1. graph f(x)=2x+1 and g(x)=−x+4 on the same coordinate plane. what is the solution to the equation f(x)=g(x) ? enter your answer in the box. 2. let f(x)=x+2f(x)=x+2 and g(x)=2x+1 . graph the functions on the same coordinate plane. what are the solutions to the equation f(x)=g(x) ? enter your answers in the boxes. 3. the functions f(x)=−2x+2 and g(x)=(13)x+1 are shown in the graph. what are the solutions to −2x+2=(13)x+1? select each correct answer. −1 0 2 3 4

Step-by-step answer

P Answered by Master

32

2x + 1 = -x + 4

x = 1

x+2 = 2x+1

x= 1

-2x+2 = 13x+1

x = 1/15

Mathematics

Me. 1. graph f(x)=2x+1 and g(x)=−x+4 on the same coordinate plane. what is the solution to the equation f(x)=g(x) ? enter your answer in the box. 2. let f(x)=x+2f(x)=x+2 and g(x)=2x+1 . graph the functions on the same coordinate plane. what are the solutions to the equation f(x)=g(x) ? enter your answers in the boxes. 3. the functions f(x)=−2x+2 and g(x)=(13)x+1 are shown in the graph. what are the solutions to −2x+2=(13)x+1? select each correct answer. −1 0 2 3 4

Step-by-step answer

P Answered by Master

32

2x + 1 = -x + 4

x = 1

x+2 = 2x+1

x= 1

-2x+2 = 13x+1

x = 1/15

Mathematics

If f(x) = x1/2 and g(x)= 2x^3 - x1/2 - x, find f(x)-g(x)

Step-by-step answer

P Answered by Specialist

8

D- f(x) - g(x) = -2 $x^{3}$ + 2 $x^{1/2}$

Step-by-step explanation:

f(x) - g(x) = ( $x^{1/2}$ - x) - (2 $x^{3}$ - $x^{1/2}$ - x)

f(x) - g(x) = $x^{1/2}$ - x - 2 $x^{3}$ + $x^{1/2}$ + x - distribute negative sign

f(x) - g(x) = -2 $x^{3}$ + 2 $x^{1/2}$ - combine like terms ( -x & +x cancel out)

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