What is the domain of f(x) = 1/(x² - 4)?

Question

Accepted Answer

All real numbers except x = 2 and x = -2. The domain excludes values where the denominator equals zero. Setting x² - 4 = 0: x² = 4, so x = 2 or x = -2. Therefore, the domain is all real numbers except x = 2 and x = -2. These excluded values correspond to vertical asymptotes of the function.

Excluding only x = 4 confuses x² - 4 = 0 with x - 4 = 0; the equation x² - 4 = 0 factors as (x-2)(x+2) = 0, giving two solutions. Claiming all real numbers ignores the restriction that division by zero is undefined; the denominator x² - 4 does equal zero for certain values of x. Excluding only x = 2 finds one solution to x² - 4 = 0 but misses the second; students must remember that squaring introduces both positive and negative roots.

Finding domains of rational functions by identifying denominator restrictions is essential for the DSST exam. Students should always factor the denominator completely and set each factor equal to zero. This process identifies all points of discontinuity and helps in graphing the function.

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