Question

Use the pair of functions to find f(g(x)) and g(f(x)) . Simplify your answers. f(x)=x−−√+4 , g(x)=x2+1

Answer 1

We have a case of composite functions, we must evaluate or replace one function as x value of the other one. In other words and doing the calculations

$\begin{gathered} f(g(x))=f(x^2+1)=\sqrt{x^2+1}+4 \\ g(f(x))=(\sqrt{x})^2+8\sqrt{x}+16+1=x+8\sqrt{x}+17 \end{gathered}$

Thus, the answer to the exercise is

f(g(x))=√(x^2+1) +4

g(f(x))=x+8√x+17