Question

use algebra to find the inverse of the function (f(x) = 3x^7 - 4)

the inverse function is (f^{-1}(x) =)

entry tip: to enter an answer like (\sqrtn{x}), type root(n)(x). preview your answer before submitting!

Explanation:

Step1: Set function to y

$$y = 3x^7 - 4$$

Step2: Swap variables

$$x = 3y^7 - 4$$

Step3: Isolate the term

$$x + 4 = 3y^7$$

Step4: Divide by coefficient

$$\frac{x + 4}{3} = y^7$$

Step5: Solve for y

$$y = \sqrt[7]{\frac{x + 4}{3}}$$

Answer:

\(f^{-1}(x) = \sqrt[7]{\frac{x+4}{3}}\)