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Examine the continuity of f(x) = x2-9x-3 on R. - Mathematics and Statistics

Sum

Examine the continuity of f(x) = `(x^2 - 9)/(x - 3)` on R.

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Solution

f(x) = `(x^2 - 9)/(x - 3)`; x ∈ R

f(x) is a rational function and is continuous for all x ∈ R, except at the points where denominator becomes zero. Here, denominator x – 3 = 0 when x = 3.
∴ Function f is continuous for all x ∈ R, except at x = 3, where it is not defined.

Concept: Continuity in the Domain of the Function
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