Question

A function f(x) = |1 – x + |x|| is :

Find the value of a and b so that function f defined as : f(x) = {(x – 2)/(|x – 2|) + a, if x < 2; a + b, if x = 2; (x – 2)/(|x – 2|) + b, if x > 2} is a continuous function.

Verify whether the function f defined by f(x) = {x sin(1/x), x ≠ 0; 0, x = 0} is continuous at x = 0 or not.

Find the values of a and b so that the following function is differentiable for all values of x : f(x) = {ax + b, x > -1; bx² - 3, x ≤ -1}