math
posted by noel on .
7. Determine the inverse of each relation given.
a. f(x) = 1/x2 + 3
b. f(x) = 2(x – 4)^2 + 5

y = 1/(x2) + 3
y3 = 1/(x2)
x2 = 1/(y3)
x = 1/(y3) + 2
so, f^{1}(x) = 1/(x3) + 2
y = 2(x4)^2 + 5
y5 = 2(x4)^2
(y5)/2 = (x4)^2
now, we can use ± root, so let's choose the + root:
√[(y5)/2] = x4
√[(y5)/2]+4 = x
so, f^{1}(x) = √[(x5)/2] + 4