Given the functions:
[tex]\begin{gathered} f(x)=x^2 \\ g(x)=x^2+4 \end{gathered}[/tex]
We will find the following composite functions:
a) f o g:
[tex]\begin{gathered} (f\circ g)(x)=(x^2+4)^2 \\ (f\circ g)(x)=x^4+8x^2+16 \end{gathered}[/tex]
The resulted function is a polynomial function
The domain of the function is all real numbers
b) g o f:
[tex]\begin{gathered} (g\circ f)(x)=(x^2)^2+4 \\ (g\circ f)(x)=x^4+4 \end{gathered}[/tex]
The domain of the function is all real numbers
c) f o f:
[tex]\begin{gathered} (f\circ f)(x)=(x^2)^2 \\ (f\circ f)(x)=x^4 \end{gathered}[/tex]
The domain of the function is all real numbers
d) g o g:
[tex]\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}[/tex]
The domain of the function is all real numbers
