LimitsHard

Question

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

Options

A.infinitely many points
B.exactly one point
C.exactly three points
D.no point

Solution

If [g(x)] = sgb(g(x)) = sgn (x(x2 - 5x + 6)) = sgn (x (x - 2) (x - 3)) =
f(g(x)) is discontinuous at 3 points (0, 2 and 3)

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