Question

Can someone help me find the inverse of the function f(x)=2x+1/2

Answer 1

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

Answer 2

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

Answer 3

please you have to find x as a function of y

Answer 4

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

Answer 5

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

Answer 6

1/2x-1/4?

Answer 7

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

Answer 8

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:
\[\Large {f^{ - 1}}\left( x \right) = \frac{1}{2}\left( {x - \frac{1}{2}} \right)\]

Answer 9

agreez
\[f(x) = 2x+ \frac{1}{2} \]
\[y = 2x+ \frac{1}{2} \]
\[x = 2y+ \frac{1}{2} \]

\[x - \frac{1}{2} = 2y \]
\[\frac{1}{2}x - \frac{1}{4} = y \]

Answer 10

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