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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

Find the inverse of the functionfx 2x3 4 5 pointsf1x cube root of x divided by two 4f1x cube root of quantity x minus four divided by twof1x cube root of quanti class=

Respuesta :

Given

[tex]f(x)=2x^3-4[/tex]

Solution

[tex]\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}[/tex]The final answerOption C[tex]f^{-1}(x)=\sqrt[3]{\frac{x+4}{2}}[/tex]

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