Q99 / 180 · KCET 2023 · Mathematics

If the function is $f(x)=\frac{1}{x+2}$, then the point of discontinuity of the composite function $y=f(f(x))$ is

  • A
    $\frac{5}{2}$
  • B
    $\frac{2}{5}$
  • C
    $\frac{1}{2}$
  • Correct answer
    D
    $\frac{-5}{2}$

Solution

$y=f(f(x))=f\left(\frac{1}{2+x}\right)$ $=\frac{1}{2+\frac{1}{2+x}}=\frac{2+x}{4+2 x+1}=\frac{2+x}{5+2 x}$ This function is not continuous at $x=-2$ (because $f(x)$ is not defined at this point) and $x=-\frac{5}{2}$ because $f(f(x))$ is not defined at this point.

Hence, the correct answer is option: 'D'.

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