SOLUTION: Find the inverse function of f f(x) = sqrt(2x-1) y=sqrt(2x-1) y^2 = 2x-1 y^2 + 1 = 2x (y^2 +1)/2 = x f^-1(x) = y^2 + 1/2 Thank you so very much!

Algebra ->  Functions -> SOLUTION: Find the inverse function of f f(x) = sqrt(2x-1) y=sqrt(2x-1) y^2 = 2x-1 y^2 + 1 = 2x (y^2 +1)/2 = x f^-1(x) = y^2 + 1/2 Thank you so very much!      Log On


   

Question 45524This question is from textbook College Algebra
: Find the inverse function of f
f(x) = sqrt(2x-1)
y=sqrt(2x-1)
y^2 = 2x-1
y^2 + 1 = 2x
(y^2 +1)/2 = x
f^-1(x) = y^2 + 1/2
Thank you so very much! This question is from textbook College Algebra

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
f(x) = sqrt(2x-1)
y=sqrt(2x-1)
Interchange x and y to get:
x=sqrt(2y-1)
Solve for y, as follows:
x^2=2y-1
y=(x^2+1)/2
y=(1/2)x^2 + (1/2) for x>=0
This is the inverse.
Cheers,
Stan H.