If f(x) = {(1, x ≤ -1)(|x|, -1 < x < 1.)(0, x ≥ 1) Then, f is A. continuous at x = –1 B. differentiable at x = –1

Question

If \(\text{f(x)} = \begin{cases} 1, & x \leq -1\\ |x|, & -1< x < 1\\ 0, & x \geq 1 \end{cases}.\) Then, f is

A. Continuous at x = –1

B. Differentiable at x = –1

C. Everywhere continuous

D. Everywhere differentiable

Answer 1

Correct answer is A and B.

Checking the continuity at x = -1:

LHL at x = -1,

Hence, f(x) is continuous at x = -1.

Checking the differentiability at x = -1:

LHD at x = -1,