1. The problem asks to find the composition of functions $(fg)(x)$ where $f(x) = 1 - x^2$ and $g(x) = 1 - x$. 2. The composition $(fg)(x)$ means $f(g(x))$, which is the function $f$ evaluated at $g(x)$. 3. Substitute $g(x)$ into $f$: $$ (fg)(x) = f(g(x)) = f(1 - x) $$ 4. Using the definition of $f(x)$, replace $x$ by $1 - x$: $$ f(1 - x) = 1 - (1 - x)^2 $$ 5. Expand the square: $$ (1 - x)^2 = (1 - x)(1 - x) = 1 - 2x + x^2 $$ 6. Substitute back: $$ f(1 - x) = 1 - (1 - 2x + x^2) $$ 7. Simplify by distributing the minus sign: $$ 1 - 1 + 2x - x^2 = 2x - x^2 $$ 8. Therefore, the composition is: $$ (fg)(x) = 2x - x^2 $$ This is the final answer.