Given that \(f(x) = \frac{x+1}{2}\), find \(f^{1}(-2)\).
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Correct Answer: Option A
Explanation:
Let \(f(x) = y\), then we have
\(y = \frac{x+1}{2} \implies 2y = x+1; x = 2y-1\)
Let \(f^{1}(x) = x; x = 2y-1\), replacing y with x,
\(f^{1}(x) = 2x - 1 \implies f^{1}(-2) = 2(-2) -1= -5\)
Let \(f(x) = y\), then we have
\(y = \frac{x+1}{2} \implies 2y = x+1; x = 2y-1\)
Let \(f^{1}(x) = x; x = 2y-1\), replacing y with x,
\(f^{1}(x) = 2x - 1 \implies f^{1}(-2) = 2(-2) -1= -5\)