Question

Let ƒ(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

We have f(g(x)) = sgn (g(x)) = sgn(x(x² – 5x + 6)) = sgn x (x – 2) (x – 3)

∴ f(g) x =

Clearly f(g(x)) is discontinuous at x = 0, 2, 3.