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If f(x) is an invertible function and g(...

If `f(x)` is an invertible function and `g(x)=2f(x)+5,` then the value of `g^(-1)(x)i s` (a)`2f^(-1)(x)-5` (b) `1/(2f^(-1)(x)+5)` `1/2f^(-1)(x)+5` (d) `f^(-1)((x-5)/2)`

A

`2f^(-1)(x)-5`

B

`(1)/(2f^(-1)(x)+5)`

C

`(1)/(2)f^(-1)(x)+5`

D

`f^(-1)((x-5)/(2))`

Text Solution

Verified by Experts

The correct Answer is:
D
Given `g(x)=2f(x)+5`
Replacing x by `g^(-1)(x)`, we get
`g(g^(-1)(x))=2f(g^(-1)(x))+5`
`rArr" "x=2 f(g^(-1)(x))+5`
`rArr" "f(g^(-1)(x))=(x-5)/(2)`
`rArr" "f^(-1)(x)=f^(-1)((x-5)/(2))`
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