## anonymous one year ago Can someone help me find the inverse of the function f(x)=2x+1/2

1. Michele_Laino

we can rewrite your function as below: $\Large y = 2x + \frac{1}{2}$ now solve that equation for x, what do you get?

2. anonymous

Replace x to y x=2y+(1/2) 2y=x - (1/2) y=(x/2)- (1/4) Inverse function is (x/2)- (1/4)

3. Michele_Laino

please you have to find x as a function of y

4. Michele_Laino

starting from my equation above, we get: 2x=y-1/2 so x=...?

5. UsukiDoll

dude I would just swap x and y and solve for y

6. anonymous

1/2x-1/4?

7. anonymous

$y=2x+\frac{ 1 }{ 2 } \rightarrow x= 2y+\frac{ 1 }{ 2 }$ now make y the subject

8. Michele_Laino

being y=f(x) and since your function admits its inverse function, then we can write: $\Large x = {f^{ - 1}}\left( y \right) = \frac{1}{2}\left( {y - \frac{1}{2}} \right)$ now, if you want to change variable, namely y--->x then we can write: $\Large {f^{ - 1}}\left( x \right) = \frac{1}{2}\left( {x - \frac{1}{2}} \right)$

9. UsukiDoll

agreez $f(x) = 2x+ \frac{1}{2}$ $y = 2x+ \frac{1}{2}$ $x = 2y+ \frac{1}{2}$ $x - \frac{1}{2} = 2y$ $\frac{1}{2}x - \frac{1}{4} = y$

10. anonymous

Ok thanks everyone I got it, you guys helped a lot! (: