## anonymous one year ago what is the inverse of the function y=5x^3?

1. anonymous

To find the inverse: Replace f(x) with y Switch x's and y's, so put x where y is and x where y is. Solve for y Replace y with f^-1(x)

2. anonymous

$y=5x^3 \implies x = 5y^3$ solve for y now

3. anonymous

so would it y=5x/3?

4. anonymous

No where did you get the 3

5. anonymous

$y^3 = \frac{ x }{ 5 }$ you will have to take the cube root not divide by 3.

6. anonymous

$\huge x^{1/3} = \sqrt[3]{x}$ cube root

7. anonymous

$\sqrt[3]{5x}$

8. anonymous

so it would be that ^ correct?

9. anonymous

Nope, you take the cube root of both sides, $\huge y^3 = \frac{ x }{ 5 } \implies y = \sqrt[3]{\frac{ x }{ 5 }} \implies f^{-1}(x) = \sqrt[3]{\frac{ x }{ 5 }}$

10. anonymous

$\large y^3 = \frac{ x }{ 5 } \implies y = \sqrt[3]{\frac{ x }{ 5 }} \implies f^{-1}(x) = \sqrt[3]{\frac{ x }{ 5 }}$

11. anonymous

thank you !!