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

Options

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))`

Answer

A

Explanation

`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)`