Question

what is the inverse of the function y=5x^3?

Answer 1

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)

Answer 2

\[y=5x^3 \implies x = 5y^3\] solve for y now

Answer 3

so would it y=5x/3?

Answer 4

No where did you get the 3

Answer 5

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

Answer 6

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

Answer 7

\[\sqrt[3]{5x}\]

Answer 8

so it would be that ^ correct?

Answer 9

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

Answer 10

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

Answer 11

thank you !!