Question

What is the inverse f(x)=3x^3-4

Answer 1

f^-1(x) =
`\sqrt[3]{(x + 4)/3}`

Explanation:

y = 3x^3 - 4 ==> solve for x

y + 4 = 3x^3 ==> isolate x by adding 4 on both sides

(y + 4)/3 = x^3 ==> divide 3 into both sides

x =
`\sqrt[3]{(y + 4)/3}` ==> isolate x by taking the cube root on both sides

y =
`\sqrt[3]{(x + 4)/3}` ==> switch both x and y

f^-1(x) =
`\sqrt[3]{(x + 4)/3}`