Question

Which of the following functions has an inverse that is not a function?

Answer 1

Answer:

the y=x^2

Step-by-step explanation:

When you do inverses, you are also doing the inverse operation. The inverse y=x is y=x. The inverse of y= 2x+1 is y= 1/2x-1/2. How did I do that? You switch y and x in the equation and then solve for y.  y= 2x+1 turns into  x= 2y+1. Subtract 1, and then divide by two. (x-1)=2y---> 1/2x-1/2. But that is still a function, right?  Then we are brought to y=x^2. The inverse operation is square rooting. y= sqrt(x). When you try to graph something square rooted you get a sideways parabola. When you draw a sideways parabola, you can see that it fails the vertical line test- so that one is not a function. Hope that helps!