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f(x)=x-5 g(x)=(x^(2)-12)/(x^(2)+4) Write g(f(x)) as an expression in terms of x. g(f(x))=

f(x)=x−5 f(x)=x-5 \newlineg(x)=x2−12x2+4 g(x)=\frac{x^{2}-12}{x^{2}+4} \newlineWrite g(f(x)) g(f(x)) as an expression in terms of x x .\newlineg(f(x))= g(f(x))=

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Q. f(x)=x−5 f(x)=x-5 \newlineg(x)=x2−12x2+4 g(x)=\frac{x^{2}-12}{x^{2}+4} \newlineWrite g(f(x)) g(f(x)) as an expression in terms of x x .\newlineg(f(x))= g(f(x))=
  1. Substitute and Find g(f(x))g(f(x)): First, we need to substitute the expression for f(x)f(x) into g(x)g(x) to find g(f(x))g(f(x)).\newlinef(x)=x−5f(x) = x - 5\newlineg(x)=x2−12x2+4g(x) = \frac{x^2 - 12}{x^2 + 4}\newlineNow, let's substitute xx in g(x)g(x) with f(x)f(x):\newlineg(f(x))=g(x−5)g(f(x)) = g(x - 5)
  2. Replace xx with f(x)f(x): Now we will replace xx in g(x)g(x) with (x−5)(x - 5):g(f(x))=(x−5)2−12(x−5)2+4g(f(x)) = \frac{(x - 5)^2 - 12}{(x - 5)^2 + 4}
  3. Expand Numerator and Denominator: Next, we expand the numerator and the denominator: g(f(x))=(x2−10x+25)−12(x2−10x+25)+4g(f(x)) = \frac{(x^2 - 10x + 25) - 12}{(x^2 - 10x + 25) + 4}
  4. Simplify the Expression: Simplify the expression by combining like terms: g(f(x))=x2−10x+13x2−10x+29g(f(x)) = \frac{x^2 - 10x + 13}{x^2 - 10x + 29}

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