Question

use algebra to find the inverse of the function $f(x)=3x^{3}+4$. the inverse function is $f^{-1}(x)=square$. entry tip: to enter an answer like $sqrtn{x}$, type root(n)(x). preview your answer before submitting! submit question

Explanation:

Step1: Replace $f(x)$ with $y$

$y = 3x^{3}+4$

Step2: Swap $x$ and $y$

$x = 3y^{3}+4$

Step3: Solve for $y$

First, subtract 4 from both sides: $x - 4=3y^{3}$. Then divide both sides by 3: $\frac{x - 4}{3}=y^{3}$. Finally, take the cube - root of both sides: $y=\sqrt[3]{\frac{x - 4}{3}}$.

Answer:

$root(3)((x - 4)/3)$