Question

Need help on this math problem!!!

Answer 1

`(fof^(-1))(x)=x`

Explanation:

Composition of two functions f(x) and g(x) is represented by,

(fog)(x) = f[g(x)]

If a function is,

f(x) = (-6x - 8)² [where x ≤
`-(8)/(6)`]

Another function is the inverse of f(x),

`f^(-1)(x)=-(√(x)+8)/(6)`

Now composite function of these functions will be,

`(fof^(-1))(x)=f[f^(-1)(x)]`

=
`[-6((√(x)+8)/(6))-8]^(2)`

=
`[-√(x)+8-8]^2`

=
`(-√(x))^2`

= x

Therefore,
`(fof^(-1))(x)=x`