# Thread: Relations and functions: Inverses

1. ## Relations and functions: Inverses

I have no idea how to do these. her is a example

If
,
then f(2) =

2. Originally Posted by pletchera
I have no idea how to do these. her is a example

If
,
then f(2) =
Hi pletchera,

$\displaystyle f(x)=3x+1$

$\displaystyle f(2)=3(2)+1$

$\displaystyle f(2)=7$

We don't need the inverse function to find f(2).

3. Originally Posted by masters
Hi pletchera,

$\displaystyle f(x)=3x+1$

$\displaystyle f(2)=3(2)+1$

$\displaystyle f(2)=7$

We don't need the inverse function to find f(2).
Makes so much sense now thank you!

but would it be the same for this one?

f (x) = 3x + 1 and f-1 = x-1/3

4. Originally Posted by pletchera
Makes so much sense now thank you!

but would it be the same for this one?

f (x) = 3x + 1 and f-1 = x-1/3
I'm not sure what you're asking but f(x) is a function of x. $\displaystyle f^{-1}(x)$ is the inverse function of x.

If you want to find f(x), simply substitute whatever x is into your function.

$\displaystyle f(x)=3x+1$

$\displaystyle f(2)=3(2)+1$

$\displaystyle f(2)=7$

If you want to find out what $\displaystyle f^{-1}(2)$ is, then

$\displaystyle f^{-1}(x)=\frac{x-1}{3}$

$\displaystyle f^{-1}(2)=\frac{2-1}{3}$

$\displaystyle f^{-1}(2)=\frac{1}{3}$

5. Also $\displaystyle f(f^{-1}(x)) = x$ by definition