Question

which of these statements best describes inverse functions?

the composition of a function and its inverse function results in the absolute value parent function, ( y = |x| ).

the composition of a function and its inverse function results in the quadratic parent function, ( y = x^2 ).

the composition of a function and its inverse function results in the identity function, ( y = 0 ).

the composition of a function and its inverse function results in the identity function, ( y = x ).

Explanation:

By definition, for a function \(f(x)\) and its inverse \(f^{-1}(x)\), the compositions \(f(f^{-1}(x)) = x\) and \(f^{-1}(f(x)) = x\) hold. This is the identity function \(y = x\), which maps every input to itself. The other options describe incorrect functions that do not result from composing a function and its inverse.

Answer:

The composition of a function and its inverse function results in the identity function, \(y = x\).