Posted by Vanilla on Saturday, April 7, 2012 at 7:36pm.
Find the inverse function of f
f(x) = x^2 + x, x >(or equal to) (1/2)
Thanks!

Math  Reiny, Saturday, April 7, 2012 at 10:30pm
let y = x^2 + x , x ≤ 1/2
the inverse is
x = y^2 + y
solving for y ...
y^2 + y  x = 0
y = (1 ± √(1  4x))/2
f(x) = 1/2 ± √(14x)/2 where x ≤ 1/4
but in the original we are only considering the left "wing" of the parabola, so in the inverse we have to consider only
f(x) = 1/2  √(14x)/2 , for x ≤ 1/4
testing:
in original, let x = 5
f(5) = 255 = 20 , point is (5,20)
in the inverse
f(20) = 1/2  √81/2 = 1/  9/2 = 5
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