A) \[2{{f}^{-1}}(x)-5\]
B) \[\frac{1}{2{{f}^{-1}}(x)+5}\]
C) \[\frac{1}{2}{{f}^{-1}}(x)=5\]
D) \[{{f}^{-1}}\left( \frac{x-5}{2} \right)\]
Correct Answer: D
Solution :
[d] Replacing \[x\] by \[{{g}^{-1}}(x)\], we get \[x=2f({{g}^{-1}}(x))+5\] \[\therefore f({{g}^{-1}}(x))=\frac{x-5}{2}\] \[\therefore {{g}^{-1}}(x)={{f}^{-1}}\left( \frac{x-5}{2} \right)\]
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