Two functions f and g are defined on the set R of real numbers by...
FURTHER MATHEMATICS
WAEC 2007
Two functions f and g are defined on the set R of real numbers by \(f : x \to 2x - 1\) and \(g : x \to x^{2} + 1\). Find the value of \(f^{-1} \circ g(3)\).
- A. 12
- B. 11
- C. \(\frac{11}{2}\)
- D. \(\frac{9}{2}\)
Correct Answer: C. \(\frac{11}{2}\)
Explanation
\(f(x) = 2x - 1; g(x) = x^{2} + 1\)
\(f(x) = 2x - 1\)
\(f(y) = 2y - 1 \)
\(x = 2y - 1 \implies 2y = x + 1\)
\(y = \frac{x + 1}{2}\)
\(g(3) = 3^{2} + 1 = 10\)
\(f^{-1}(10) = \frac{10 + 1}{2} = \frac{11}{2}\)
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