Question

The point(s) of discontinuity of the composite function y = f (f(x)) , where $f\left(x\right)=\frac{1}{x-1}$ is/are

• A. x = 1
• B. x = 0
• C. x = 2
• D. x = -2

Answer 1

Answer: (A), (C)

The correct options are
A x = 1
C x = 2

We know that $f\left(x\right)=\frac{1}{x-1}$ is discontinuous at x = 1.
Now, for
$f\left[f\right(x\left)\right]=f\left(\frac{1}{x-1}\right)=\frac{1}{\frac{1}{x-1}-1}=\frac{x-1}{2-x}.\mathrm{which}\mathrm{is}\mathrm{discontinuous}\mathrm{at}x=2.$
Hence, the points of discontinuity are x = 1 and x = 2.