precalc
posted by Anonymous on .
find the inverse of the function
f(x) = x^2 − 6x, x ≥ 3

Your given function will be the part of the parabola which lies to the right of the vertex (3, 9)
so y = x^2  6x
inverse is
x = y^2 6y
y^2  6y = x
complete the square:
y^2  6y+ 9 = x+9
(y3)^2= x+9
y  3= ± √(x+9)
y = 3 ± √(x+9)
but we only used the part for x≥3 of the original, so
the inverse is
f^1 (x) = 3 + √(x+9) , x ≥ 9
check:
let x = 4
f(4) = 16  24 = 8
f^1 (8) = 3 + √(8+9)
= 3 + √1 = 4
let x = 5.67
f(5.67) = 1.8711
f^1 (1.8711) = 3 + √(1.8711+9)
= 3+√7.1289
=3 + 2.67
= 5.67
I am very confident my inverse is correct!