Question:
Given the function f (x) = 1/(x + 2) . Find the points of discontinuity of the composite function
y = f (f (x)).
Solution:
Given,
$f(x)=\frac{1}{x+2}$
$f[f(x)]=\frac{1}{f(x)+2}=\frac{1}{\frac{1}{x+2}+2}=\frac{1}{\frac{1+2 x+4}{x+2}}=\frac{x+2}{2 x+5}$
$\therefore f[f(x)]=\frac{x+2}{2 x+5}$
Now, the function will not be defined and continuous where
2x + 5 = 0 ⇒ x = -5/2
Therefore, x = -5/2 is the point of discontinuity.
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