Read the two statements and choose the correct option.
I. $f(x) = [x^{2}]$ is continuous at $x = 0$ .
II. $g(x) = [x]^{2}$ is continuous at $x = 0$ .

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: for $-1 < x < 1$ , $0 \le x^{2} < 1$ , so $[x^{2}] = 0$ all around 0, equal to $f(0)$ . True.
II: just left of 0, $[x] = -1$ , so $[x]^{2} = 1$ ; at 0 and to its right, $[x]^{2} = 0$ . A jump, so false.

Worth noting

The order matters: in $[x^{2}]$ the input of the greatest integer function never crosses an integer near 0.

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

Read the two statements and choose the correct option.I. f(x)=[x2]f(x) = [x^{2}]f(x)=[x2] is continuous at x=0x = 0x=0.II. g(x)=[x]2g(x) = [x]^{2}g(x)=[x]2 is continuous at x=0x = 0x=0.