Question

If G^-1(x) is the inverse of G(x), what is the value of G^-1(G(x))?

Answer 1

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

Explanation:

Definition: Let f be one-to-one function with the domain A and the range B. Then the inverse function
`f^(-1)` has the domain B and the range A and is defined as

`f^(-1)(y)=x\ \Leftrightarrow \ f(x)=y`

Facts:

1) For every
`x\in A:`

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

2) For every
`y\in B:`

`f(f^(-1)(y))=y`

So,
`G^(-1)(G(x))=x`