First slide

Continuity

Question

The number of points of discontinuity of y = f(x) where $f (x) = \frac{3}{2 u^{2} + 5 u - 3}$ and $u = \frac{1}{x + 2}$ is

Moderate

A

2
B

3
C

4
D

5

Solution

u is discontinuous at x = - 2, f(x) is discontinuous
at $u = \frac{1}{2}, - 3 when u = - 3 \Rightarrow x = - \frac{7}{3}, u = \frac{1}{2} \Rightarrow x = 0$
Hence f is discontinuous at $x = - \frac{7}{3}, - 2, 0$

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