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

Assessment: WAEC SSCE - Further Mathematics - 2006 (Objective) Subject: Further Mathematics

Question 1 Report

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

Answer Details
To find \(f^{-1}(-\frac{1}{2})\), we need to find the value of x such that \(f(x) = -\frac{1}{2}\). We know that \(f(x) = \frac{1}{2 - x}\), so we set \(\frac{1}{2 - x} = -\frac{1}{2}\) and solve for x: \[\frac{1}{2 - x} = -\frac{1}{2}\] \[2 - x = -2\] \[x = 4\] Therefore, \(f^{-1}(-\frac{1}{2}) = 4\). Note that we were able to solve for \(f^{-1}(y)\) by first setting \(y = f(x)\), then solving for x. This is because the inverse function of f, denoted by \(f^{-1}\), is defined such that \(f^{-1}(f(x)) = x\) for all x in the domain of f.
Read lesson note on Rational Functions (WAEC)
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