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=(x+4)/(2) \\ \\ y=\sqrt[3]{(x+4)/(2)} \end{gathered}`The final answerOption C
`f^(-1)(x)=\sqrt[3]{(x+4)/(2)}`