Given the funcation f(x)=1 x+2 . Find the points of discontinuity… - Vidyadip

Question

Given the funcation $\text{f(x)}=\frac{1}{\text{x}+2}.$ Find the points of discontinuity of the function f(f(x)).

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Answer

$\text{f}\big[\text{f(x)}\big]=\frac{1}{\frac{1}{\text{x}+2}+2}=\frac{\text{x}+2}{2\text{x}+5}$
So, f[f(x)] is not defind at x + 2 = 0 and 2x + 5 = 0
If x + 2, then x = - 2
If 2x + 5 = 0, then $\text{x}=-\frac{5}{2}$
Hence, the function is dicontinuous at $\text{x}=-\frac{5}{2}$ and -2

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