Example

Evaluating the Fourth Root Function f(x)=5x44f(x) = \sqrt[4]{5x - 4}

To evaluate the fourth root function f(x)=5x44f(x) = \sqrt[4]{5x - 4} for specific values, substitute the value for the independent variable xx and simplify using the order of operations:

  • Evaluate f(4)f(4): Substitute 44 for xx to obtain f(4)=5(4)44f(4) = \sqrt[4]{5(4) - 4}. Multiply to get 2044\sqrt[4]{20 - 4}, which simplifies to 164\sqrt[4]{16}. Taking the fourth root yields f(4)=2f(4) = 2.
  • Evaluate f(12)f(-12): Substitute 12-12 for xx to obtain f(12)=5(12)44f(-12) = \sqrt[4]{5(-12) - 4}. Multiply to get 6044\sqrt[4]{-60 - 4}, which simplifies to 644\sqrt[4]{-64}. Because the fourth root of a negative number is not a real number, the function does not have a value at x=12x = -12.

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Updated 2026-05-26

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