Question

Let f(x) = sgn (x) and g(x) = x (x² – 5x + 6). The function f(g(x)) is discontinuous at

• A. Infinitely many points
• B. Exactly one point
• C. Exactly three points
• D. No point

Answer 1

Answer: (C)

Exactly three points

Answer 2

g(x) = x (x – 3) (x – 2)

From wavy curve when

x < 0 g(x) < 0 sgn (g(x)) =  – 1

x = 0 g(x) = 0 sgn (g(x)) = 0

0 < x < 2 g(x) > 0 sgn(g(x)) = + 1

x = 2 g(x) = 0 sgn (g(x)) = 0

2 < x < 3 g(x) < 0 sgn (g(x)) = – 1

x = 3 g(x) = 0 sgn (g(x)) = 0

x > 3 g(x) > 0 sgn (g(x)) = + 1

Clearly f(g(x)) discontinuous at three points.

x = – 1, 0, + 1