Question 4 of 11, Step 1 of 1
Correct

Find a formula for the inverse of the following function, if possible.
\[
V(x)=\left(x^{3}-3\right)^{\frac{1}{3}}-1
\]

Answer
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\[
V^{-1}(x)=
\]
does not have an inve

Step 1 ：Replace \(V(x)\) with \(y\) to get \(y = (x^{3} - 3)^{\frac{1}{3}} - 1\).

Step 2 ：Swap \(x\) and \(y\) to get \(x = (y^{3} - 3)^{\frac{1}{3}} - 1\).

Step 3 ：Solve for \(y\) to get the inverse function. The equation becomes \(x = ((y^{3} - 3)^{\frac{1}{3}} - 1)^{3} - 3)^{\frac{1}{3}} - 1\).

Step 4 ：Solving this equation gives three roots, but we are interested in the real root. The real root is the first element in the list of roots.

Step 5 ：The inverse of the function is \(V^{-1}(x)=1.44224957030741*(0.333333333333333*(x + 1.0)^{3} + 1)^{\frac{1}{3}}\).

Step 6 ：\(\boxed{V^{-1}(x)=1.44224957030741*(0.333333333333333*(x + 1.0)^{3} + 1)^{\frac{1}{3}}}\) is the final answer.