anonymous
  • anonymous
Help please f(x) = cubed root 3x^3-1 find f^-1(x) and (f^-1 of) (135)
Mathematics
katieb
  • katieb
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asnaseer
  • asnaseer
the easiest way of tackling problems like this is to write them in the form y=f(x), then swap the x and y's and finally solve for y. so, in this case we are given:\[y=f(x)=\sqrt[3]{3x^3-1}\]so first step is to swap the x and y's, giving us:\[x=\sqrt[3]{3y^3-1}\]now we need to solve for y. so lets cube both sides to get:\[x^3=3y^3-1\]therefore:\[y=\sqrt[3]{\frac{1+x^3}{3}}\]this is your inverse function. so now replace y with \(f^{-1}(x)\) to get:\[f^{-1}(x)=\sqrt[3]{\frac{1+x^3}{3}}\] to work out \(f^{-1}(135)\) just substitute x=135 into the equation above.
anonymous
  • anonymous
thankyou very much!
asnaseer
  • asnaseer
yw

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anonymous
  • anonymous
can i ask one more question for a different problem : f(x)=2x+3 find (f(x))^-1
asnaseer
  • asnaseer
Its best if you post this as a new question.
asnaseer
  • asnaseer
but the principal to solve it the same as I outlined for you above.

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