Question

If R(x) and S(x) are inverse functions, which statement must be true? A) R(S(X))=1 B) R(S(X))=X C) R(X) R(X)= 1/S(x) D) R(x)=-S(x)

Answer 1

the answer will be B)R(S(X))=X

Answer 2

ANSWER: The correct answer is
`R(S(x))=x`.

Step-by-step explanation

The composition of a function of
`x` and its inverse will produce the independent variable
`x`.

For instance, let
`f(x)=2x`.

The inverse of this function is
`f^(-1)(x)=(x)/(2)`.

If we compose these two functions, we will obtain;

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

This means we have to substitute the whole inverse function in to the function itself.

`(f\circ f^(-1))(x)=f(f^(-1)(x))=2((x)/(2))=x`

The other way round will also produce the same result.

Thus;

`(f^(-1)\circ f(x)=f^(-1)(f(x))=((2x)/(2))=x`

This does not only apply to the given example it applies to all functions and their inverse.