A function f is defined on R, the set of real numbers, by: \(f :
FURTHER MATHEMATICS
WAEC 2008
A function f is defined on R, the set of real numbers, by: \(f : x \to \frac{x + 3}{x - 2}, x \neq 2\), find \(f^{-1}\).
- A. \(f^{-1} : x \to \frac{2x + 3}{x - 1}, x \neq 1\)
- B. \(f^{-1} : x \to \frac{x + 3}{x + 2}, x \neq -2\)
- C. \(f^{-1} : x \to \frac{x - 1}{2x + 3}, x \neq -\frac{3}{2}\)
- D. \(f^{-1}: x \to \frac{x - 2}{x + 3}, x \neq -3\)
Correct Answer: A. \(f^{-1} : x \to \frac{2x + 3}{x - 1}, x \neq 1\)
Explanation
\(f(x) = \frac{x + 3}{x - 2}\)
\(f(y) = \frac{y + 3}{y - 2}\)
Let f(y) = x,
\(x = \frac{y + 3}{y - 2}\)
\(x(y - 2) = y + 3\)
\(xy - y = 2x + 3 \implies y(x - 1) = 2x + 3\)
\(y = \frac{2x + 3}{x - 1}\)
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