Question

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

Answer 1

the value of G^-1(G(x)) is x

Explanation:

We define G^-1(x) as the inverse of G(x), when we talk about functions inverse does not work like with the numbers, this means that G^-1(x) is not equal to 1/G(x).

Inverse means that if:

G(x) = y

then:

G^-1(y) = x

then if we have:

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

so when we evaluate a given function in its inverse, the result is the input of the function.

And is the same in the case:

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

Answer 2

x

Explanation:

If you multiply a function and its inverse, you will will always get x back.

f-1( f(x) ) = x