SOLUTION: hi, i am needing help with this question from a hand out.. f:R to R is defined by f(x)=2x+1 then f^-1= i came up with 2x-1 as my answer..can you help verify? thanks

Algebra ->  Rational-functions -> SOLUTION: hi, i am needing help with this question from a hand out.. f:R to R is defined by f(x)=2x+1 then f^-1= i came up with 2x-1 as my answer..can you help verify? thanks      Log On


   

Question 74163: hi, i am needing help with this question from a hand out..
f:R to R is defined by f(x)=2x+1 then f^-1=

i came up with 2x-1 as my answer..can you help verify? thanks
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First switch the x and y variables
y=2x%2B1->x=2y%2B1 and then solve for y to find the inverse function
x-1=2y%2Bcross%281-1%29
%28x-1%29%2F2=%28cross%282%29y%29%2Fcross%282%29Divide both sides by 2
y=%281%2F2%29x-%281%2F2%29There's the inverse function.


To check this let x=1 and plug it into the original equation
y=2%281%29%2B1
y=2%2B1
y=3
Take this answer and plug it into the inverse function
y=%281%2F2%29%283%29-%281%2F2%29
y=%283%2F2%29-%281%2F2%29
y=%282%2F2%29
y=1
Since you got the number you originally plugged in (which was 1) this shows us that this is the inverse function.