Question

Suppose that fis a one-to-one function, and fis its inverse. Suppose alsothat h(x) = 4 and g(x) = x2 + xsecx. Then which of the following do we NOTknow to be true?

Answer 1

We know h(x) and g(x)

$\begin{gathered} h(x)=4 \\ g(x)=x^2 \end{gathered}$

And also we know that f(x) is a one-to-one function, and f^-1 is its inverse.

We can use the properties of compound functions to reduce problems.

A.

$(g\circ h\circ f^{-1})(x)$

We can calculate

$g\circ h$

But, we don't know the exact value of f^-1. So we cannot know if the equality is true.

Finally, the answer is letter A.

For the rest options we can calculate them using the properties of compound functions.