If \(f(x) = \frac{4}{x} - 1, x \neq 0\), find \(f^{-1}(7)\).
FURTHER MATHEMATICS
WAEC 2016
If \(f(x) = \frac{4}{x} - 1, x \neq 0\), find \(f^{-1}(7)\).
- A. \(\frac{-3}{7}\)
- B. \(0\)
- C. \(\frac{1}{2}\)
- D. \(4\)
Correct Answer: C. \(\frac{1}{2}\)
Explanation
\(f(x) = \frac{4}{x} - 1\). Let y = f(x)
\(y = \frac{4 - x}{x} \implies xy + x = 4\)
\(x(y + 1) = 4 \therefore x = \frac{4}{y + 1}\)
\(f^{-1}(7) = \frac{4}{7 + 1} = \frac{1}{2}\)
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