Domain Math Example 1

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Example 1

easy
Find the domain of f(x)=x−3f(x) = \sqrt{x - 3}.

Solution

  1. 1
    The expression under a square root must be non-negative: x−3≥0x - 3 \geq 0.
  2. 2
    Solve: x≥3x \geq 3.
  3. 3
    The domain is [3,∞)[3, \infty).

Answer

[3,∞)[3, \infty)
Square root functions require non-negative radicands. Setting the expression inside the root ≥0\geq 0 and solving gives the domain.

About Domain

The domain of a function is the complete set of allowable input values for which the function produces a defined, valid output.

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More Domain Examples

Example 2 medium

Find the domain of [formula].

Example 3 medium

Find the domain of [formula].

Example 4 hard

Find the domain of [formula].

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