Example Question 2

Example corresponding to question 2 in college algebra 2.

Example 1


If $f(x)=x^3-2$, what is the inverse function of $f(x)$?

  1. $\sqrt[3]{x}$


  2. $\sqrt[3]{x+2}$


  3. $\sqrt[3]{x-2}$


  4. $\dfrac{\sqrt[3]{x}}{2}$


  5. $x+2$

Solution


  1. To find the inverse of a function, we need to write the function in the form of an equation as follows

    $y=x^3-2$


  2. Then interchange $x$ and $y$ in the equation obtained

    $x=y^3-2$


  3. Then solve for $y$

    $y^3=x+2$

    $y=\sqrt[3]{x+2}$

  4. The inverse of $f$ is given by

    $f^{-1}(x)=\sqrt[3]{x+2}$

    Answer B