Example

Evaluating the Cube Root Function h(x)=5x23h(x) = \sqrt[3]{5x - 2}

To evaluate the cube root function h(x)=5x23h(x) = \sqrt[3]{5x - 2} for specific values, substitute the value for the independent variable xx and simplify using the order of operations:

  • Evaluate h(2)h(2): Substitute 22 for xx to obtain h(2)=5(2)23h(2) = \sqrt[3]{5(2) - 2}. Multiply to get 1023\sqrt[3]{10 - 2}, which simplifies to 83\sqrt[3]{8}. Taking the cube root yields h(2)=2h(2) = 2.
  • Evaluate h(5)h(-5): Substitute 5-5 for xx to obtain h(5)=5(5)23h(-5) = \sqrt[3]{5(-5) - 2}. Multiply to get 2523\sqrt[3]{-25 - 2}, which simplifies to 273\sqrt[3]{-27}. Taking the cube root yields h(5)=3h(-5) = -3.

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Updated 2026-05-25

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