Question

If $f\left(x\right)=\frac{1}{(2-x)}$then the points of discontinuity of the composite function $y=f\left(f\left(x\right)\right)$ are

• A. $2,\frac{3}{4}$
• B. $1,2$
• C. $2,3$
• D. $2,\frac{3}{2}$

Answer 1

Answer: (D)

$2,\frac{3}{2}$

$y=f\left(f\left(x\right)\right)=f\left(\frac{1}{2-x}\right)=\frac{1}{2-\frac{1}{2-x}}=\frac{2-x}{3-2x}$
This function is not continuous at $x=2$ (because $f\left(x\right)$ is not defined at this point), and $x=\frac{3}{2}$ (because $f\left(f\left(x\right)\right)$ is not defined at this point.