SOLUTION: f(x)=(6x-7)^3+5 find f^-1(x)

Algebra ->  Functions -> SOLUTION: f(x)=(6x-7)^3+5 find f^-1(x)      Log On


   

Question 366586: f(x)=(6x-7)^3+5
find f^-1(x)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
The idea is to first replace f(x) with y, and then swap x and y. From there, solve for y to find the inverse function. So...

f%28x%29=%286x-7%29%5E3%2B5


y=%286x-7%29%5E3%2B5


x=%286y-7%29%5E3%2B5


x-5=%286y-7%29%5E3


root%283%2Cx-5%29=6y-7


root%283%2Cx-5%29%2B7=6y


%281%2F6%29%28root%283%2Cx-5%29%2B7%29=y


y=%281%2F6%29%28root%283%2Cx-5%29%2B7%29


This means that the inverse function is