The composite function $g \circ f$ is a constant function if

• Correct answer
  A

  $f(x)=\left(\cos ^{-1} x, \sin ^{-1} x\right)$ and $g(x, y)=x+y$
• Correct answer
  B

  $f(x)=[x]$ and $g(x)=x-[x]$, where $[x]$ denotes the largest integer less than or equal to $x$.
• Correct answer
  C

  $f(x)=\frac{x}{|x|}$ and $g(x)=\cos \left(\frac{\pi}{2} x\right)$
• D

  $f(x)=|\sin x|$ and $g(x)=x-[x]$.

Hence, the correct answer is options: 'A', 'B', 'C'.