Read the two statements and choose the correct option.
I. If $f$ and $g$ are continuous everywhere, so is $f \circ g$ .
II. $f(x) = \frac{1}{x^{2} - 4}$ is continuous at $x = 2$ .

Only ICorrect answerYour answerOnly IICorrect answerYour answerBoth I and IICorrect answerYour answerNeither I nor IICorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

I: a composition of continuous functions is continuous. True.
II: 2 is not in the domain, so $f$ has no value there to be continuous with. False.

Worth noting

A rational function is continuous on its domain, which leaves out the zeros of its denominator.

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

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

Read the two statements and choose the correct option.I. If fff and ggg are continuous everywhere, so is f∘gf \circ gf∘g.II. f(x)=1x2−4f(x) = \frac{1}{x^{2} - 4}f(x)=x2−41​ is continuous at x=2x = 2x=2.