Let $f(x) = x^{2}$ and $g(x) = \cos x$ . Which of these functions is not continuous at every real $x$ ?

\frac{f}{g}

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g \circ f

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f \cdot g

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f - g

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Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

Sums, differences, products and compositions of functions continuous everywhere are continuous everywhere.
$\frac{f}{g}$ needs $\cos x \ne 0$ : at $x = \frac{\pi}{2}$ it is not even defined, so it is not continuous there.

Worth noting

$g \circ f = \cos(x^{2})$ is a composition of continuous functions, so it is continuous everywhere.

Ten questions from Continuity & Differentiability, at your own pace.

Ten questions from Continuity & Differentiability, at your own pace.

Let f(x)=x2f(x) = x^{2}f(x)=x2 and g(x)=cos⁡xg(x) = \cos xg(x)=cosx. Which of these functions is not continuous at every real xxx?