Question 187708
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(400,300,-10,10,-10,10,8x^3-1,(1/2)(x+1)^(1/3))}}}
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Cheers,
Stan H.