Let f(x) = 1 - x,g(x) = frac{1}{1 - x},and h( | vedclass

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(B) Given $f(x) = 1 - x$,$g(x) = \frac{1}{1 - x}$,and $h(x) = \frac{1}{x}$.We are given the equation $f(F(h(x))) = g(x)$.Substituting the expressions

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$F(2022) = g(2022)$

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(B) Given $f(x) = 1 - x$,$g(x) = \frac{1}{1 - x}$,and $h(x) = \frac{1}{x}$.We are given the equation $f(F(h(x))) = g(x)$.Substituting the expressions for $f$ and $g$,we get $1 - F(h(x)) = \frac{1}{1 - x}$.Rearranging for $F(h(x))$,we have $F(h(x)) = 1 - \frac{1}{1 - x} = \frac{1 - x - 1}{1 - x} = \frac{-x}{1 - x} = \frac{x}{x - 1}$.Let $t = h(x) = \frac{1}{x}$. Then $x = \frac{1}{t}$.Substituting $x = \frac{1}{t}$ into the expression for $F(h(x))$,we get $F(t) = \frac{1/t}{1/t - 1} = \frac{1/t}{(1 - t)/t} = \frac{1}{1 - t}$.Thus,$F(x) = \frac{1}{1 - x} = g(x)$.Therefore,$F(2022) = g(2022)$.

Let $f(x) = 1 - x$,$g(x) = \frac{1}{1 - x}$,and $h(x) = \frac{1}{x}$ be three functions,for $x \neq 0, 1$. If a function $F(x)$ satisfies $f(F(h(x))) = g(x)$,then which of the following is true?

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