Question

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

Answer 1

Answer:

$G^{-1}(G(x))=x$

Step-by-step 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, $G^{-1}(G(x))=x$