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What is the domain of the radical function f(x) = √(2x² - 5x - 12)?

User TEXHIK
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Final answer:

The domain of the function f(x) = √(2x² - 5x - 12) is x ≤ -3/2 or x ≥ 4.

Step-by-step explanation:

The domain of the radical function f(x) = √(2x² - 5x - 12) can be determined by finding the values of x that make the expression inside the square root non-negative. This means the expression 2x² - 5x - 12 must be greater than or equal to zero.

To solve this inequality, we can factor the quadratic and find the x-values that satisfy the inequality. The factored form of the quadratic is (2x + 3)(x - 4). We set each factor equal to zero and solve for x to find the critical points.

  • (2x + 3) = 0, x = -3/2
  • (x - 4) = 0, x = 4

The domain of the function is the set of all x-values that satisfy the inequality. We test intervals between the critical points and use test values to determine the sign of the expression. The domain is x ≤ -3/2 or x ≥ 4.

User Alessandro Fazzi
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