if f is a one-to-one function such that f(2)=9, what is f^-1 (9)?

Question

concidering that i have no idea what a one-to-one function is, i find it rather difficult to asnwer this question, but my guess is -2... but i have no idea.

Answer 1

A function f satisftying the equation f(x) = y is one to one if a single value of x yields only a single value of y.
If f(2) = 9, then f^(-1)(9) = 2.
The 'graph' of this function passes through the point (2, 9) and that is all you know about it.
Given x = 2, you know that y = 9.
The inverse function works the other way round.
Given x = 9, the function requires that y = 2.
In general if y = f(x), then x = f^(-1)(y).

Answer 2

2
When x = 2, f(x) = 9
So when f(x) = 9, x = 2.

"One - to - one" means that if you choose x, I can tell you what y is equal to AND if you tell me what y is, then I can tell you what x was.

For example in
y = x + 1
if x = 3, y = 4 and if y = 4, then x = 3.

An example of a function that is NOT one-to-one would be
y = x^2
This is because, for example, x = 5, then y = 25.
However, if x = -5, then y = 25 as well.
So if y = 25, I cannot tell you what x is equal to. It could be EITHER 5 or -5.

I hope this helps!

Answer 3

2..one to one refers to the mapping of x values to y values.

This means there is only ONE unique value for f^-1 (9)

Answer 4

Operation with f
2 •-------->• 9

Operation with f^(-1)
2 •<-------• 9

Thus f^(-1) (9) = 2