Restricted Domain Math Example 1

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Example 1

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

Solution

  1. 1
    The square root function requires a non-negative argument: x−3≥0x - 3 \ge 0.
  2. 2
    Solve: x≥3x \ge 3.
  3. 3
    The domain is [3,∞)[3, \infty).

Answer

[3,∞)[3, \infty)
A restricted domain limits the inputs of a function to a subset of all real numbers. For square roots, the expression under the radical must be non-negative. For fractions, the denominator cannot be zero. These natural restrictions come from the mathematical definition of the operations involved.

About Restricted Domain

Restricting a domain limits allowable inputs so a function has desired properties, often invertibility.

Learn more about Restricted Domain →

More Restricted Domain Examples

Example 2 medium

Restrict the domain of [formula] so that the function has an inverse. Find the inverse on this restr

Example 3 medium

Find the domain of [formula].

Example 4 hard

Restrict the domain of [formula] to the largest interval containing [formula] on which [formula] is

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