Question

Hae friends, will you show that the function y=x^2 is not one to one?

Answer 1

When x = 1, y = ...?

Answer 2

When x = -1, y = ...?

Answer 3

To show something is one-to-one, you would need to show that f(a) = f(b) if and only if a = b. So basically we're just showing that this is not true.

f(a): (a)^2
f(b): (b)^2

a^2 = b^2
square root both sides and you get
\[a = \pm b\], which shows the function is not one-to-one.

Answer 4

When x=1,y =1

Answer 5

when x=-1, y=1

Answer 6

See! You have two different inputs generating the same output!

Answer 7

yes!

Answer 8

By definition, it is not one to one.

Answer 9

Graphically x^2 fails the horizontal line test. The graph of a one to one MUST only intersect the horizontal line once and only once!

Answer 10

thanks guys!