Questions: MAT100-08 COLLEGE ALGEBRA 2024-3 10.09 - Values of Inverse F... CURRENT OBJECTIVE Given table of values of a function, find value of inverse function Question Given the following table of values for the function (f(x)), determine (f^-1(-5)). (x) -5 1 4 5 6 8 (f(x)) -11 -9 -7 -5 -2 10 Provide your answer below: [ f^-1(-5)= ]

Solution Steps

To find the value of the inverse function \( f^{-1}(-5) \), we need to determine the value of \( x \) for which \( f(x) = -5 \) using the given table. We will look through the table to find the corresponding \( x \) value.

We are tasked with finding \( f^{-1}(-5) \). This means we need to determine the value of \( x \) such that \( f(x) = -5 \).

From the given table of values: \[ \begin{array}{c|cccccc} x & -5 & 1 & 4 & 5 & 6 & 8 \\ \hline f(x) & -11 & -9 & -7 & -5 & -2 & 10 \end{array} \] we observe that \( f(5) = -5 \). Therefore, the corresponding \( x \) value for which \( f(x) = -5 \) is \( x = 5 \).

Thus, we conclude that: \[ f^{-1}(-5) = 5 \]

Final Answer