Problem 49 of 7
Find the inverse of the cube-root function f(x)=cuberoot(2x-6).
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solve by cubing and transform domain/range.
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Solve by cubing and transform domain/range.
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Solution
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1. Swap x and y.
2. Isolate the cube-root term.
3. Cube both sides and solve for y.
4. State that unrestricted cube-root parent functions have all-real domain and range.
Use the worked steps, then substitute the final answer back into the original relationship to confirm it satisfies the prompt.
Adding square-root branch restrictions to cube-root inverses.