Domain Math Example 4

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Example 4

hard
Find the domain of f(x)=ln⁡(9−x2)f(x) = \ln(9 - x^2).

Solution

  1. 1
    The argument of a logarithm must be strictly positive: 9−x2>09 - x^2 > 0.
  2. 2
    Rearrange: x2<9x^2 < 9, so −3<x<3-3 < x < 3.
  3. 3
    The domain is (−3,3)(-3, 3).

Answer

(−3,3)(-3, 3)
Logarithmic functions require strictly positive inputs. Solving the inequality 9−x2>09 - x^2 > 0 determines where the function is defined.

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 1 easy

Find the domain of [formula].

Example 2 medium

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Example 3 medium

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