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Let agt1 be a real number and f(x)=log(a...

Let `agt1` be a real number and `f(x)=log_(a)x^(2)" for "xgt 0.` If `f^(-1)` is the inverse function of f and b and c are real numbers then `f^(-1)(b+c)` is equal to

A

`f^(-1)(b).f^(-1)(c)`

B

`f^(-1)(b)+f^(-1)(c)`

C

`(1)/(f(b+c))`

D

`(1)/(f^(-1)(b)+f^(-1)(c))`

Text Solution

Verified by Experts

The correct Answer is:
A
`y=2log_(a^(x))`
`rArr" "log_(a)x=(y)/(2)`
`rArr" "x=a^(y//2)`
`rArr" "f^(-1)(y)=a^(y//2)`
`rArr" "f^(-1)(b+c)=a^((b+c)/(2))=a^((b)/(2)).a^((c)/(2))=f^(-1)(b).f^(-1)(c)`
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