Which of these functions are continuous at every real x? I. f(x) = | x - 1 | + | x - 2 | II. f(x) = | sin x | III. f(x) = [x], the greatest integer function IV. f(x) = cos | x |

Question 65

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Which of these functions are continuous at every real $x$ ?
I. $f(x) = \lvert x - 1 \rvert + \lvert x - 2 \rvert$
II. $f(x) = \lvert \sin x \rvert$
III. $f(x) = [x]$ , the greatest integer function
IV. $f(x) = \cos \lvert x \rvert$

All four: I, II, III and IVCorrect answerYour answerI and IV onlyCorrect answerYour answerII and IV onlyCorrect answerYour answerI, II and IV onlyCorrect answerYour answer

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CorrectNot quiteAnswer D

Correct answer: D

Sums and compositions of continuous functions are continuous: I, II and IV.
III jumps at every integer.

Worth noting

A corner, as in $\lvert x - 1 \rvert$ at 1, spoils differentiability, not continuity.

Concept: Recognising continuous functions
Typical timeTypical: 120 s
Your timeYours: —

The rule this testsContinuous functions

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