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Hello, May I please get some assistance with this homework question? I posted an image below. Parts A and B are already completed. Q2 (Part C.)

Hello, May I please get some assistance with this homework question? I posted an image-example-1

1 Answer

2 votes

SOLUTION

The given functions are


f(x)=4x+3,g(x)=x^2

Recall the rule of composite function


f\circ g=f(g(x))

a. f o g

This can be rewritten as


f\circ g=f(g(x))

Substitute the value of g(x) into the expression

This gievs


f(g(x))=f(x^2)

Substitute x² for x into the expression


f(x^2)=4x^2+3

Therefore fog is


4x^2+3

The domain of fog is all real numbers

Following the same procedure it follows

b.


\begin{gathered} \text{gof}=g(f(x)) \\ =g(4x+3) \\ =(4x+3)^2 \end{gathered}

The domain of gof is all real numbers

c. fof


\begin{gathered} f\circ f=f(f(x)) \\ =f(4x+3) \\ =4(4x+3)+3 \\ =16x+12+3 \\ =16x+15 \end{gathered}

The domain of fof is all real numbers

d. gog


\begin{gathered} g\circ g=g(g(x)) \\ =g(x^2) \\ =(x^2)^2 \\ =x^4 \end{gathered}

The domain of gog is all real numbers

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