Question

The domain of the derivative of the functions

f(x) = tan-1 x, if |x| ≤ 1

f(x) = (1/2)(|x| - 1), if |x| > 1

is

(a) R - {0}

(b) R - {1}

(c) R - {-1}

(d) R - {-1, 1}

Answer 1

Correct option (d) R - {-1, 1}

Explanation :

f(x) is discontinuous at x = - 1 and x = 1

.'. Domain of f'(x) ∈ R - {-1, 1}