7. Determine the inverse of each relation given.

Question

a. f(x) = 1/x-2 + 3

b. f(x) = 2(x – 4)^2 + 5

Answer 1

y = 1/(x-2) + 3
y-3 = 1/(x-2)
x-2 = 1/(y-3)
x = 1/(y-3) + 2

so, f^-1(x) = 1/(x-3) + 2

y = 2(x-4)^2 + 5
y-5 = 2(x-4)^2
(y-5)/2 = (x-4)^2
now, we can use ± root, so let's choose the + root:
√[(y-5)/2] = x-4
√[(y-5)/2]+4 = x

so, f^-1(x) = √[(x-5)/2] + 4