SOLUTION: Hi, I'm trying to find the inverse function of: f(x) = 8x^3 - 1 Not really sure how to approach this one. I've plotted points on a graph and took the inverses of those points, bu

Algebra ->  Inverses -> SOLUTION: Hi, I'm trying to find the inverse function of: f(x) = 8x^3 - 1 Not really sure how to approach this one. I've plotted points on a graph and took the inverses of those points, bu      Log On


   

Question 187708This question is from textbook Precalculus
: Hi,
I'm trying to find the inverse function of: f(x) = 8x^3 - 1
Not really sure how to approach this one. I've plotted points on a graph and took the inverses of those points, but I can't come up with a function to get those points.
Thanks,
Lynn This question is from textbook Precalculus

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
find the inverse function of: f(x) = 8x^3 - 1
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When it comes to functions, inverse means "interchange the x and the y values
in all the points. So, if f has point (1,2), f^-1 will have point (2,1).
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You have y = 8x^3-1
1st: Interchange x and y to get
x = 8y^3-1
2nd Solve for y
8y^3 = x+1
y^3 = (x+1)/8
y = [cbrt(x+1)]/2
That is the inverse of y = 8x^3-1
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I'll graph both so you can see how interchanging x and y looks on a graph.
graph%28400%2C300%2C-10%2C10%2C-10%2C10%2C8x%5E3-1%2C%281%2F2%29%28x%2B1%29%5E%281%2F3%29%29
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Cheers,
Stan H.