Which of the following statements is not true? A. The graph of \( f^{-1} \) is a reflection of the graph of \( f \) about the line \( y=x \). B. If a function \( f \) has an inverse function, then we can find the inverse function by replacing \( f(x) \) with \( y \), interchanging the variables \( x \) and \( y \), and solving for \( x \). C. The function \( f^{-1} \) exists if and only if the function \( f \) is one-to-one. D. To verify that two one-to-one functions, \( f \) and \( g \), are inverses of each other, we must show that \( f(g(x))=g(f(x))=x \).

To determine which statement is not true, let's analyze each one: A. **The graph of \( f^{-1} \) is a reflection of the graph of \( f \) about the line \( y=x \).** - This statement is true. The inverse function \( f^{-1} \) can be obtained by reflecting the graph of \( f \) across the line \( y = x \). B. **If a function \( f \) has an inverse function, then we can find the inverse function by replacing \( f(x) \) with \( y \), interchanging the variables \( x \) and \( y \), and solving for \( x \).** - This statement is true. This is the standard method for finding the inverse of a function. C. **The function \( f^{-1} \) exists if and only if the function \( f \) is one-to-one.** - This statement is true. A function must be one-to-one (injective) in order to have an inverse function. D. **To verify that two one-to-one functions, \( f \) and \( g \), are inverses of each other, we must show that \( f(g(x))=g(f(x))=x \).** - This statement is not entirely accurate. While it is true that to verify that \( f \) and \( g \) are inverses, you need to show that \( f(g(x)) = x \) and \( g(f(x)) = x \), the statement implies that both functions must be one-to-one, which is not necessary for the verification of their inverse relationship. The requirement is that \( f \) and \( g \) must be inverses of each other, but they do not need to be one-to-one for the verification process itself. Thus, the statement that is not true is: **D.** To verify that two one-to-one functions, \( f \) and \( g \), are inverses of each other, we must show that \( f(g(x))=g(f(x))=x \).