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

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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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