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Example 1
If $f(x)=x^3-2$, what is the inverse function of $f(x)$?
- $\sqrt[3]{x}$
- $\sqrt[3]{x+2}$
- $\sqrt[3]{x-2}$
- $\dfrac{\sqrt[3]{x}}{2}$
- $x+2$
Solution
- To find the inverse of a function, we need to write the function in the form of an equation as follows
$y=x^3-2$
- Then interchange $x$ and $y$ in the equation obtained
$x=y^3-2$
- Then solve for $y$
$y^3=x+2$
$y=\sqrt[3]{x+2}$
- The inverse of $f$ is given by
$f^{-1}(x)=\sqrt[3]{x+2}$
Answer B
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