Inverse of a reciprocal-type function and a second function found from a composite condition
Inverse of a reciprocal-type function and a second function found from a composite condition
6 marks
Let \(f(x)=3+\dfrac{5}{2x-1}\) for all real \(x\) with \(x\neq\dfrac12\).
- Determine the inverse function, giving \(f^{-1}(x)\) in terms of \(x\).[3]
A second function \(g\) has the property that \((f\circ g)(2x)=x\) wherever both sides are defined.
- Hence, or otherwise, write \(g(x)\) as a single fraction in \(x\).[3]
Solution:
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Answer:(a) \(f^{-1}(x)=\dfrac{x+2}{2x-6}\) (b) \(g(x)=\dfrac{x+4}{2x-12}\)
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