Example

Evaluating the Cube Root Function g(x)=3x43g(x) = \sqrt[3]{3x - 4}

To evaluate the cube root function g(x)=3x43g(x) = \sqrt[3]{3x - 4} for specific values, substitute the value for the independent variable xx and simplify using the order of operations:

  • Evaluate g(4)g(4): Substitute 44 for xx to obtain g(4)=3(4)43g(4) = \sqrt[3]{3(4) - 4}. Multiply to get 1243\sqrt[3]{12 - 4}, which simplifies to 83\sqrt[3]{8}. Taking the cube root yields g(4)=2g(4) = 2.
  • Evaluate g(1)g(1): Substitute 11 for xx to obtain g(1)=3(1)43g(1) = \sqrt[3]{3(1) - 4}. Multiply to get 343\sqrt[3]{3 - 4}, which simplifies to 13\sqrt[3]{-1}. Taking the cube root yields g(1)=1g(1) = -1.

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Updated 2026-05-26

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