f(x)=7x+2 g(x)=(x^(2))/(x-5) Write (g@f)(x) as an expression in terms of x. (g@f)(x)=

Understand (g@f)(x): First, let's understand what (g@f)(x) means. It means we need to apply the function g to the result of the function f applied to x. In other words, we need to substitute f(x) into g(x) wherever we see an x in g(x).Write Functions: Now let's write down the functions f(x) and g(x) to see what we're working with: f(x) = 7x + 2 g(x) = x^2 / (x - 5)Substitute f(x) into g(x): We need to substitute f(x) into g(x). This means wherever we see an x in g(x), we replace it with 7x + 2: (g@f)(x) = (7x + 2)^2 / ((7x + 2) - 5)Simplify the Expression: Now let's simplify the expression: (g@f)(x) = (7x + 2)^2 / (7x + 2 - 5) (g@f)(x) = (7x + 2)^2 / (7x - 3)Express in Terms of x: We have now expressed (g@f)(x) in terms of x. There is no further simplification needed unless we want to expand the numerator, which is not required by the question prompt.

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f(x)=7x+2

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

(g@f)(x)=

$f(x)=7 x+2$ $\newline$ $g(x)=\frac{x^{2}}{x-5}$ $\newline$ Write $(g \circ f)(x)$ as an expression in terms of $x$ . $\newline$ $(g \circ f)(x)=$

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Math Problems

Algebra 1

Compare linear and exponential growth

Full solution

f(x)=7 x+2

\newline

g(x)=\frac{x^{2}}{x-5}

\newline

Write

(g \circ f)(x)

as an expression in terms of

x

\newline

(g \circ f)(x)=

Understand $(g@f)(x)$ : First, let's understand what $(g@f)(x)$ means. It means we need to apply the function $g$ to the result of the function $f$ applied to $x$ . In other words, we need to substitute $f(x)$ into $g(x)$ wherever we see an $x$ in $g(x)$ .
Write Functions: Now let's write down the functions $f(x)$ and $g(x)$ to see what we're working with: $\newline$ $f(x) = 7x + 2$ $\newline$ $g(x) = \frac{x^2}{x - 5}$
Substitute $f(x)$ into $g(x)$ : We need to substitute $f(x)$ into $g(x)$ . This means wherever we see an $x$ in $g(x)$ , we replace it with $7x + 2$ :
$(g@f)(x) = \frac{(7x + 2)^2}{(7x + 2) - 5}$
Simplify the Expression: Now let's simplify the expression: $\newline$ $(g@f)(x) = \frac{(7x + 2)^2}{(7x + 2 - 5)}$ $\newline$ $(g@f)(x) = \frac{(7x + 2)^2}{(7x - 3)}$
Express in Terms of x: We have now expressed $(g@f)(x)$ in terms of $x$ . There is no further simplification needed unless we want to expand the numerator, which is not required by the question prompt.