Question

Can someone help with this please????

Answer 1

Given:

The given function is:

`f(x)=11x-11`

To find:

The value of
`(f\circ f^(-1))(-11)`.

Solution:

We have,

`f(x)=11x-11`

First we have to find the inverse of this function.

Putting f(x)=y, we get

`y=11x-11`

Interchange x and y.

`x=11y-11`

Isolate the variable y.

`x+11=11y`

`(x+11)/(11)=y`

`y=(x+11)/(11)`

Putting
`y=f^(-1)(x)`, we get

`f^(-1)(x)=(x+11)/(11)`

Now,

`(f\circ f^(-1))(-11)=f(f^(-1)(-11))`

`(f\circ f^(-1))(-11)=f\left((-11+11)/(11)\right)`
`\left[\because f^(-1)(x)=(x+11)/(11)\right]`

`(f\circ f^(-1))(-11)=f\left((0)/(11)\right)`

`(f\circ f^(-1))(-11)=f\left(0\right)`

The given function is
`f(x)=11x-11`.

`(f\circ f^(-1))(-11)=11(0)-11`

`(f\circ f^(-1))(-11)=-11`

Therefore, the value of
`(f\circ f^(-1))(-11)` is
`-11`. Hence the correct option is A.