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If f(x)="log"(7)(x)/(8) for x ge 8, the...

If `f(x)="log"_(7)(x)/(8)` for `x ge 8`, then for the values x of its domain , `f^(-1)(x)` =

A

`8(7^(x))`

B

`7(8^(x))`

C

`8(7^(x+1))`

D

`"log"_(7)(x)/(8)`

Text Solution

Verified by Experts

The correct Answer is:
A
Set `u = "log"_(7)(x)/(8)`. To find the inverse, switch the values of x and y and then solve for y :
`x = "log"_(7)(y)/(8)`
This is equalent to
`7^(x)=(y)/(8)`
`8(7^(x))=y`
Therefore, `f^(-1)(x)=8(7^(x))`.
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