Question

Select the correct answer from each drop-down menu.In the first box it’s either (equal to) or (not equal to)In the Second box it’s either (are) or (are not)

Answer 1

To find h(k(x)), we have to replace the x-variable of h(x) with the function k(x).

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

Then, find k(h(x)) using the same process.

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

As you can observe, the functions obtained are not equal.

Therefore, h(k(x)) is not equal to k(h(x)).

Also, the functions h and k are not inverse functions because the coefficient 5 would be as a denominator.