Given the functions:
[tex]\begin{gathered} f(x)=x²+1 \\ g(x)\sqrt{x}-1 \end{gathered}[/tex]
to find the composition f(g(x)), we have to evaluate the whole expression for g inside of f. Then, we get the following:
[tex]\begin{gathered} (f\circ g)(x)=f(g(x))=f(\sqrt{x}+1)=(\sqrt{x}-1)²+1 \\ =x-2\sqrt{x}+2 \end{gathered}[/tex]
therefore, f(g(x)) = x -2sqrt(x)+2 which is different than f(g(x)) = x.
