If \(f(x) = \frac{4}{x} – 1, x \neq 0\), find \(f^{-1}(7)\).
- \(\frac{-3}{7}\)
- \(0\)
-
\(\frac{1}{2}\)
- \(4\)
The correct answer is: C
Explanation
\(f(x) = \frac{4}{x} - 1\). Let y = f(x)
\(y = \frac{4 - x}{x} \implies xy + x = 4\)
\(x(y + 1) = 4 \therefore x = \frac{4}{y + 1}\)
\(f^{-1}(7) = \frac{4}{7 + 1} = \frac{1}{2}\)