Question

what is the value of $f^{-1}(-6)$ when $f(x) = \frac{5}{2}x + 6$?
enter your response here: blank box

Explanation:

Step1: Recall the definition of inverse function

To find \( f^{-1}(-6) \), we know that if \( y = f(x) \), then \( x = f^{-1}(y) \). So we need to find the \( x \) such that \( f(x)=-6 \).

Step2: Set up the equation

Set \( f(x)=\frac{5}{2}x + 6=-6 \).

Step3: Solve for \( x \)

Subtract 6 from both sides: \(\frac{5}{2}x=-6 - 6=-12\).

Multiply both sides by \(\frac{2}{5}\): \(x=-12\times\frac{2}{5}=\frac{-24}{5}=-4.8\)

Answer:

\(-\frac{24}{5}\) (or -4.8)