For square root functions like f(x) = √(3x+2), the radicand (3x+2) must be greater than or equal to zero for the function to be defined in real numbers, requiring the inequality 3x+2 ≥ 0 to be solved, which yields x ≥ -2/3; unlike square roots, cube roots can accept negative inputs since odd roots of negative numbers exist as real numbers.
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DOMAIN of √(3x+2): Why You Must Solve the INEQUALITY 3x + 2 ≥ 0!Added:
When you see a square root, you want the input to be greater than or equal to zero.
If you see a cube root, then it doesn't matter. Cube roots of negative numbers, when we're dealing only with real numbers, do exist (as real numbers): cube root of -8 is -2.
But with square roots, we want the input to be greater than or equal to 0 (in Calculus 1 (or Precalculus), unless your teacher decides to do imaginary and complex numbers).
Solve for x. Subtract two from both sides.
With addition and subtraction, we do not change the direction of the inequality.
With multiplication or division by a positive number, you also do not change the direction of the inequality. Again, if this had been a -3 and I had divided both sides by -3, then the inequality would have changed to a less than or equal.
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