Question

Please help me i have tried this for two days

Answer 1

Given the functions:

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

We will find the following composite functions:

a) f o g:

$\begin{gathered} (f\circ g)(x)=(x^2+4)^2 \\ (f\circ g)(x)=x^4+8x^2+16 \end{gathered}$

The resulted function is a polynomial function

The domain of the function is all real numbers

b) g o f:

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

The domain of the function is all real numbers

c) f o f:

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

The domain of the function is all real numbers

d) g o g:

$\begin{gathered} (g\circ g)(x)=(x^2+4)^2+4 \\ (g\circ g)(x)=x^4+8x^2+16+4 \\ \\ (g\circ g)(x)=x^4+8x^2+20 \end{gathered}$

The domain of the function is all real numbers