The inverse of a function is given by \(f^{-1} : x \to \frac{x + 1}{4}\).
FURTHER MATHEMATICS
WAEC 2011
The inverse of a function is given by \(f^{-1} : x \to \frac{x + 1}{4}\).
- A. \(f : x \to 4x - 1\)
- B. \(f : x \to 4x + 1\)
- C. \(f : x \to \frac{4x - 1}{4}\)
- D. \(f : x \to \frac{x - 1}{2}\)
Correct Answer: A. \(f : x \to 4x - 1\)
Explanation
The inverse of the inverse of a function gives the function
i.e \(f^{-1}(f^{-1}(x)) = f(x)\)
\(f^{-1}(x) = \frac{x + 1}{4}\)
Take y = x, so
\(f^{-1}(y) = \frac{y + 1}{4}\)
Let \(x = f^{-1}(y)\),
\(x = \frac{y + 1}{4} \implies 4x = y + 1\)
\(y = f(x) = 4x - 1\)
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