Question

F−1(f(x)) = f(f−1(x)) =

Answer 1

Given:

`f^(-1)(f(x))=f(f^(-1)(x))=?`

To find:

The missing value.

Solution:

We have,

`f^(-1)(f(x))=f(f^(-1)(x))=?` ...(i)

We know that, if
`f(x)` is a function and
`f^(-1)(x)` is its inverse function, then

`f^(-1)(f(x))=f(f^(-1)(x))=x` ...(ii)

From (i) and (ii), we get

Missing value =
`x`

Therefore, the missing value is
`x`, i.e.,
`f^(-1)(f(x))=f(f^(-1)(x))=x`.