Question

Find the inverse of the function.f(x) = 2x3 − 4 (5 points)f−1(x) = cube root of x divided by two + 4f−1(x) = cube root of quantity x minus four divided by twof−1(x) = cube root of quantity x plus four divided by twoNot a one-to-one function

Answer 1

Given

$f(x)=2x^3-4$

Solution

$\begin{gathered} Replace\text{ f\lparen x\rparen with y} \\ y=2x^3-4 \\ interchange\text{ x and y} \\ x=2y^3-4 \\ make\text{ y the subject} \\ x+4=2y^3 \\ 2y^3=x+4 \\ \\ y^3=\frac{x+4}{2} \\ \\ y=\sqrt[3]{\frac{x+4}{2}} \end{gathered}$The final answerOption C$f^{-1}(x)=\sqrt[3]{\frac{x+4}{2}}$