Question

Help please
f(x) = cubed root 3x^3-1
find f^-1(x)
and
(f^-1 of) (135)

Answer 1

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.

Answer 2

thankyou very much!

Answer 3

yw

Answer 4

can i ask one more question for a different problem :
f(x)=2x+3
find (f(x))^-1

Answer 5

Its best if you post this as a new question.

Answer 6

but the principal to solve it the same as I outlined for you above.