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