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

Understanding Composition of Functions: First, we need to understand the composition of functions. The composition (h@g)(x) means we should plug g(x) into h for every x. So we start by writing down the functions we have: g(x) = 9 + 4x h(x) = (x + 21) / 5Substituting g(x) into h(x): Now we will substitute g(x) into h(x) for every x. This means wherever we see an x in h(x), we replace it with the expression for g(x): (h@g)(x) = h(g(x)) = ((9 + 4x) + 21) / 5Simplifying the Expression: Next, we simplify the expression inside the parentheses: (9 + 4x + 21) / 5 = (30 + 4x) / 5Final Simplification: Finally, we simplify the expression by dividing each term inside the parentheses by 5: (30/5) + (4x/5) = 6 + (4/5)x

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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)=

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

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Algebra 1

Compare linear and exponential growth

Full solution

g(x)=9+4 x

\newline

h(x)=\frac{x+21}{5}

\newline

Write

(h \circ g)(x)

as an expression in terms of

x

\newline

(h \circ g)(x)=

Understanding Composition of Functions: First, we need to understand the composition of functions. The composition $(h@g)(x)$ means we should plug $g(x)$ into $h$ for every $x$ . So we start by writing down the functions we have: $\newline$ $g(x) = 9 + 4x$ $\newline$ $h(x) = \frac{x + 21}{5}$
Substituting $g(x)$ into $h(x)$ : Now we will substitute $g(x)$ into $h(x)$ for every $x$ . This means wherever we see an $x$ in $h(x)$ , we replace it with the expression for $g(x)$ : $(h\circ g)(x) = h(g(x)) = \frac{(9 + 4x) + 21}{5}$
Simplifying the Expression: Next, we simplify the expression inside the parentheses: $\newline$ egin{equation}( $9$ + $4$ x + $21$ ) / $5$ = ( $30$ + $4$ x) / $5$ egin{equation}
Final Simplification: Finally, we simplify the expression by dividing each term inside the parentheses by $5$ : $(\frac{30}{5}) + (\frac{4x}{5}) = 6 + (\frac{4}{5})x$