Question

use the drop - down menu to create true statements. if the graph of an inverse passes the origin, you know that the inverse is a function. the graph of an inverse is the reflection of the graph of the function over the line y = x. the composition of a function and its inverse is always x. the range values of an inverse are the values of the original function.

Explanation:

1. The graph of an inverse function is the reflection of the graph of the original function over the line \(y = x\). This is a fundamental property of inverse - functions in mathematics.
2. If the graph of an inverse passes through the origin, we know that the original function also passes through the origin because of the symmetry about the line \(y=x\).
3. The range values of an inverse function are the domain values of the original function, and vice - versa.
4. The composition of a function \(f\) and its inverse \(f^{-1}\) is always \(x\), i.e., \(f(f^{-1}(x))=x\) and \(f^{-1}(f(x)) = x\) for all \(x\) in the appropriate domains.

Answer:

1. The graph of an inverse is the reflection of the graph of the function over the line \(y = x\).
2. If the graph of an inverse passes the origin, you know that the original function passes the origin.
3. The range values of an inverse are the domain values of the original function.
4. The composition of a function and its inverse is always \(x\).