If \(f(x) = \frac{4}{x} - 1, x \neq 0\), find \(f^{-1}(7)\).

If \(f(x) = \frac{4}{x} - 1, x \neq 0\), find \(f^{-1}(7)\).

Answer Details

To find \(f^{-1}(7)\), we need to find the value of \(x\) for which \(f(x) = 7\). So, we start by setting \(f(x) = 7\) and solving for \(x\): \begin{align*} f(x) &= 7 \\ \frac{4}{x} - 1 &= 7 \\ \frac{4}{x} &= 8 \\ x &= \frac{4}{8} \\ x &= \frac{1}{2} \end{align*} Therefore, \(f^{-1}(7) = \frac{1}{2}\). So, the correct option is: - \(\frac{1}{2}\)