Let $f(x)=1-x, g(x)=\frac{1}{1-x}, h(x)=\frac{1}{x}$ be three functions, for $x \neq 0$, 1. If a function $F(x)$ satisfies $f(F(h(x)))=g(x)$, then

• A

  $F(2022)=f(2022)$
• Correct answer
  B

  $F(2022)=g(2022)$
• C

  $F(2022)=h(2022)$
• D

  $F(2022)=\frac{1}{2022} f(2022)$

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