SOLUTION: how to find the inverse of f(x)= sqrt((x^2)+8x) thanks :)

Algebra ->  Inverses -> SOLUTION: how to find the inverse of f(x)= sqrt((x^2)+8x) thanks :)      Log On


   

Question 262565: how to find the inverse of f(x)= sqrt((x^2)+8x) thanks :)
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
here is the original equation:
f%28x%29=+sqrt%28%28x%5E2%29%2B8x%29
let f(x) = y and then reverse all x and y variables to get
x=+sqrt%28%28y%5E2%29%2B8y%29
step 1 - square both sides to get
x%5E2+=+y%5E2+%2B+8y
now x^2 is a constant, so we can set = 0 as
y%5E2+%2B+8y+-+x%5E2+=+0
using the quadratic formula, we get
y+=+%28-8+%2B-+sqrt%2864+%2B+4%2A1%2Ax%5E2%29%29%2F2
factor a 4 out of the sqrt to get
y+=+%28-8+%2B-2sqrt%2816%2Bx%5E2%29%29%2F2
reduce to get
y%5E%28-1%29+=+%28-4+%2B-sqrt%2816%2Bx%5E2%29%29