Problem

Consider the function $f$, which is a one-to-one function with values $f(-11)=5$ and $f(-8)=-1$. Which of the following must be true? Select all correct answers. Select all that apply: $f^{-1}(5)=-11$ $f^{-1}(-1)=-11$ $f^{-1}(5)=-1$ $f^{-1}(-8)=1$ $f^{-1}(-1)=-8$ $f^{-1}(-11)=-5$

Solution

Step 1 :The function \(f\) is given as a one-to-one function. This means that for each input, there is exactly one output, and for each output, there is exactly one input.

Step 2 :We are given that \(f(-11)=5\) and \(f(-8)=-1\).

Step 3 :The inverse function \(f^{-1}\) is defined such that if \(f(a)=b\), then \(f^{-1}(b)=a\).

Step 4 :So, from the given values, we can determine that \(f^{-1}(5)=-11\) and \(f^{-1}(-1)=-8\).

Step 5 :Therefore, the correct answers are \(\boxed{f^{-1}(5)=-11}\) and \(\boxed{f^{-1}(-1)=-8}\).

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Source: https://solvelyapp.com/problems/zwm0JknxpO/

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