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g(x)=9+4x h(x)=(x+21)/(5) Write (h@g)(x) as an expression in terms of x. (h@g)(x)=

g(x)=9+4x g(x)=9+4 x \newlineh(x)=x+215 h(x)=\frac{x+21}{5} \newlineWrite (h∘g)(x) (h \circ g)(x) as an expression in terms of x x .\newline(h∘g)(x)= (h \circ g)(x)=

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Q. g(x)=9+4x g(x)=9+4 x \newlineh(x)=x+215 h(x)=\frac{x+21}{5} \newlineWrite (h∘g)(x) (h \circ g)(x) as an expression in terms of x x .\newline(h∘g)(x)= (h \circ g)(x)=
  1. Understanding Composition of Functions: First, we need to understand the composition of functions. The composition (h@g)(x)(h@g)(x) means we should plug g(x)g(x) into hh for every xx. So we start by writing down the functions we have:\newlineg(x)=9+4xg(x) = 9 + 4x\newlineh(x)=x+215h(x) = \frac{x + 21}{5}
  2. Substituting g(x)g(x) into h(x)h(x): Now we will substitute g(x)g(x) into h(x)h(x) for every xx. This means wherever we see an xx in h(x)h(x), we replace it with the expression for g(x)g(x):(h∘g)(x)=h(g(x))=(9+4x)+215(h\circ g)(x) = h(g(x)) = \frac{(9 + 4x) + 21}{5}
  3. Simplifying the Expression: Next, we simplify the expression inside the parentheses: \newlineegin{equation}(99 + 44x + 2121) / 55 = (3030 + 44x) / 55egin{equation}
  4. Final Simplification: Finally, we simplify the expression by dividing each term inside the parentheses by 55:(305)+(4x5)=6+(45)x(\frac{30}{5}) + (\frac{4x}{5}) = 6 + (\frac{4}{5})x

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