Question

Let m is the number of non-differentiable points of f(x) = ||x| – 1| and n is the number of points of differeniable of g (x) = 1/(log |x|), find the value of (m + n).

Answer 1

Given f(x) = ||x| – 1|

Clearly, f is non differentiable at x = – 1, 0, 1

Thus, m = 3 Also, g(x) = 1/log|x|

So, g(x) is not defined at x = – 1, 0, 1

Thus g(x) is discontinuous at x = – 1, 0, 1

So, n = 3

Hence, the value of (m + n) is 6.