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If \(f(x) = \frac{1}{2 - x}, x \neq 2\), find \(f^{-1}(-\frac{1}{2})\).

Further Mathematics
WAEC 2006

If \(f(x) = \frac{1}{2 - x}, x \neq 2\), find \(f^{-1}(-\frac{1}{2})\).

  • A. 4
  • B. 0
  • C. -2
  • D. -4
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NECO June/July 2024 - Get offline past questions & answers - Download objective & theory, all in one app 48789
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Correct Answer: Option A
Explanation

\(f(x) = \frac{1}{2 - x}, x \neq 2\)

\(f(y) = \frac{1}{2 - y}\)

\(x = \frac{1}{2 - y}\) (Let x = f(y))

\(2x - xy = 1 \implies y = \frac{2x - 1}{x}\)

\(\therefore f^{-1}(x) = \frac{2x - 1}{x}\)

\(f^{-1}(-\frac{1}{2}) = \frac{2(-\frac{1}{2}) - 1}{-\frac{1}{2}}\)

= \(-2 \times -2 = 4\)


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