Question

True/False: One to one functions are invertible.

Answer 1

I don't know what one to one function is...

Answer 2

true in fact only one to one functions have an inverse

Answer 3

If a function is not one-to-one, it does not have a true inverse. hence true

Answer 4

http://www.regentsprep.org/Regents/math/algtrig/ATP5/OntoFunctions.htm

Answer 5

A one-to-one function is a function in which one input is only paired with one output.
For example, y=x^2 is not a one to one function because, say, both (1)^2 and (-1)^2 yield one.

Actually, all functions are "invertible" but only one-to-one functions have inverses that are functions.

Answer 6

True. And if you want to go further, by restricting the domain of f(x) you can make a function such as f(x)=x^2 invertible.

Answer 7

Thanks everyone, I really do appreciate it but I'm trying to figure out why'd they used the word invertible though? Was that a trick?

Answer 8

Thats an actual term. It means that you can invert the graph of a one-to-one function over the y-axis to get its inverse.

Answer 9

You can read about function inverses. If a function turns an input x into an output y, then the inverse of that function maps y back to x.

For example: y=x^2. If we restrict the domain of y=x^2 to values of x greater or equal to 0, then the inverse of y=x^2 is y=sqrt(x).

For a value, say, 3. y=x^2 turns 3 into 9. However, y=sqrt(x) inverts, or turns 9 back into 3. You follow me?

Answer 10

Okay @EdG I don't understand the last sentence you wrote. And yes @anhhuyalex

Answer 11

So everything cool?

Answer 12

My mistake. Graphically, a function and its inverse are symmetric with respect to the y-axis. So when you "flip" a function over the y-axis, the resulting graph is its inverse. It's basically what anhhuyalex said, i just made it more complicated. It helps when you are working with graphs instead of equations

Answer 13

Oh, okay. Thanks so much everyone! I really do appreciate it :-). I'm preparing for my finals, sigh :(...