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 $R(S(x))=x$.

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 $f^{-1}(x)=\frac{x}{2}$.

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.

$(f\circ f^{-1})(x)=f(f^{-1}(x))=2(\frac{x}{2})=x$

The other way round will also produce the same result.

Thus;

$(f^{-1}\circ f(x)=f^{-1}(f(x))=(\frac{2x}{2})=x$

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