Question

Options for the first box are: not equal to, equal to Options for the second box are: are not, are

Answer 1

Let's find the compositions to determine wether or not they are equal:

$\begin{gathered} h(k(x))=5(\sqrt[]{5x+1})^2-1 \\ =5(5x+1)-1 \\ =25x+5-1 \\ =25x+4 \end{gathered}$

and

$\begin{gathered} k(h(x))=\sqrt[]{5(5x^2-1)+1} \\ =\sqrt[]{25x^2-5+1} \\ =\sqrt[]{25x^2-4} \end{gathered}$

From this results we conclude that the composite functions are not equal.

Now, from the previous result we conclude that they are not inverse functions. This comes from the fact