Question

Is y=x^2 a function? Is the inverse of y=x^2 a function? Justify your answer

Answer 1

Do you know the inverse of y=x^2 first of all?

Answer 2

Is it x = y?

Answer 3

swap the x and y in f(x) to get f^-1(x)
x=y^2, solve for y

Answer 4

\[y= \pm \sqrt{x}\]

Answer 5

so you're going to have 2 y values for each x-value that is not 0

Answer 6

is that a function?

Answer 7

In a function, each member of the domain corresponds to at most 1 member of the range

Answer 8

No it's not.

Answer 9

right, and is y=x^2 a function?

Answer 10

No, because it's a parabola?

Answer 11

it is a parabola, as is the inverse, but in this case, each x in the domain (all real numbers) corresponds to exactly one member of the range

Answer 12

You can use the vertical line test

Answer 13

How so?

Answer 14

Oh ok