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{:[f(x)=13-x],[h(x)=x^(2)-6x-18]:} Write (f@h)(x) as an expression in terms of x. (f@h)(x)=

f(x)=13−xh(x)=x2−6x−18 \begin{array}{l} f(x)=13-x \\ h(x)=x^{2}-6 x-18 \end{array} \newlineWrite (f∘h)(x) (f \circ h)(x) as an expression in terms of x x .\newline(f∘h)(x)= (f \circ h)(x)=

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Q. f(x)=13−xh(x)=x2−6x−18 \begin{array}{l} f(x)=13-x \\ h(x)=x^{2}-6 x-18 \end{array} \newlineWrite (f∘h)(x) (f \circ h)(x) as an expression in terms of x x .\newline(f∘h)(x)= (f \circ h)(x)=
  1. Substitute h(x)h(x) into f(x)f(x): To find the composition of the functions (f∘h)(x)(f \circ h)(x), we need to substitute the function h(x)h(x) into the function f(x)f(x). This means we will replace every instance of xx in f(x)f(x) with the expression for h(x)h(x).
  2. Write down the functions: First, let's write down the functions again for clarity:\newlinef(x)=13−xf(x) = 13 - x\newlineh(x)=x2−6x−18h(x) = x^2 - 6x - 18\newlineNow, we will substitute h(x)h(x) into f(x)f(x):\newline(f@h)(x)=f(h(x))=13−(x2−6x−18)(f@h)(x) = f(h(x)) = 13 - (x^2 - 6x - 18)
  3. Distribute the negative sign: Next, we simplify the expression by distributing the negative sign inside the parentheses: \newline(f@h)(x)=13−x2+6x+18(f@h)(x) = 13 - x^2 + 6x + 18
  4. Combine like terms: Finally, we combine like terms to get the simplified expression for (f@h)(x)(f@h)(x):(f@h)(x)=31−x2+6x(f@h)(x) = 31 - x^2 + 6x

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