Question

The function f(x) = |x| + |x – 2| is ______.

Options

• continuous, but not differentiable at x = 0 and x = 2.

• differentiable but not continuous at x = 0 and x = 2.

• continuous but not differentiable at x = 0 only.

• neither continuous nor differentiable at x = 0 and x = 2.

Answer 1

The function f(x) = |x| + |x – 2| is continuous, but not differentiable at x = 0 and x = 2.

Explanation:

f (x) = |x| + |x − 2|

To break modulus 

Put x = 0

& x − 2 = 0

Now `f(x) = {{:(-x-x+2 = -2x+2;x<0),(x-x+2=2;0≤x≤2),(x+x-2 = 2x-2;x>2):}`

by plotting the graph, we get

so f(x) is continuous everywhere but not differentiable at x = 0 and x = 2