Given the function f (x) = 1/(x + 2) .
Question:

Given the function (x) = 1/(+ 2) . Find the points of discontinuity of the composite function

((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.