Question

Which function does NOT have an inverse? Explain.

a. y = x²
b. y = x³
c. y = x
d. y = 25 - x
e. y = 1/2x

Answer 1

The function that does not have an inverse is y = x², as it fails the horizontal line test, which means it is not one-to-one and there isn't a unique inverse for every output.

Step-by-step explanation:

To determine which function does not have an inverse, we need to look for a function that does not pass the horizontal line test. This test checks whether any horizontal line would intersect the graph of the function more than once. If it does intersect the graph more than once, the function is not one-to-one and therefore does not have a unique inverse.

Among the options given:

• y = x² does not have an inverse because its graph, a parabola, is not one-to-one and fails the horizontal line test. This means for a given y there could be two possible x values (one positive and one negative).
• y = x³, y = x, y = 25 - x, and y = 1/2x are all one-to-one functions and thus pass the horizontal line test, meaning they each have an inverse.

So, the function that does not have an inverse is a. y = x².