Question

is the inverse of the function shown below also a function? explain your answer.

Explanation:

Step1: Recall function - inverse function concept

A function has an inverse that is also a function if and only if the original function is one - to - one. A one - to - one function passes the horizontal line test.

Step2: Apply horizontal line test

If we draw horizontal lines across the given graph, any horizontal line will intersect the graph at most once. This means the original function is one - to - one.

Step3: Determine inverse property

Since the original function is one - to - one, its inverse is also a function.

Answer:

Yes, the inverse of the function shown is also a function because the original function passes the horizontal line test, indicating it is one - to - one.