SOLUTION: My problem is to find an inverse of the function f(x)=(3x+7)^3-5. I know this is started as y=(3x+7)^3-5. What steps follow and what is the answer? Thanks for your help!

Algebra ->  Inverses -> SOLUTION: My problem is to find an inverse of the function f(x)=(3x+7)^3-5. I know this is started as y=(3x+7)^3-5. What steps follow and what is the answer? Thanks for your help!      Log On


   

Question 166272: My problem is to find an inverse of the function f(x)=(3x+7)^3-5. I know this is started as y=(3x+7)^3-5. What steps follow and what is the answer? Thanks for your help!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
y=%283x%2B7%29%5E3-5 Start with the given equation


x=%283y%2B7%29%5E3-5 Switch 'x' and 'y'. The goal now is to solve for 'y'


x%2B5=%283y%2B7%29%5E3 Add 5 to both sides.


root%283%2Cx%2B5%29=3y%2B7 Take the cube root of both sides to eliminate the exponent of '3'


3y%2B7=root%283%2Cx%2B5%29 Rearrange the equation


3y=root%283%2Cx%2B5%29-7 Subtract 7 from both sides


y=%28root%283%2Cx%2B5%29-7%29%2F3 Divide both sides by 3 to isolate (ie solve for) 'y'


So the inverse function is