## anonymous 4 years ago Help please f(x) = cubed root 3x^3-1 find f^-1(x) and (f^-1 of) (135)

1. 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.

2. anonymous

thankyou very much!

3. asnaseer

yw

4. anonymous

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

5. asnaseer

Its best if you post this as a new question.

6. asnaseer

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