Question

Assume the given function is one-to-one. Find the indicated value:If f(3)=2 then f^{-1}(2)=AnswerIf f^{-1}(-2)=-1 then f(-1)=?Answer

Answer 1

The question asks us to perform the inverse of two functions.

To solve this question, we need to understand how the inverse of a function works.

The inverse of a function is defined thus:

$\begin{gathered} \text{if }f(x)=y \\ x=f^{-1}(y) \end{gathered}$

With this definition, we can solve the questions.

Question 1:

$\begin{gathered} f(3)=2 \\ \therefore f^{-1}(2)=3_{} \end{gathered}$

Question 2:

$\begin{gathered} f^{-1}(-2)=-1_{} \\ \\ \therefore f(-1)=-2 \end{gathered}$

Thus, the answers are

$\begin{gathered} \text{Question 1:} \\ f^{-1}(2)=3 \\ \\ \text{Question 2:} \\ f(-1)=-2 \end{gathered}$