{:[g(x)=(8x-1)/(x+4)],[h(x)=3x+10]:} Write (g@h)(x) as an expression in terms of x. (g@h)(x)=

Understanding (g@h)(x): First, we need to understand what (g@h)(x) means. The notation (g@h)(x) represents the composition of the functions g and h, which means we need to substitute the output of h(x) into the function g. So, we will first find h(x) and then substitute it into g(x).Finding h(x): Let's find h(x). The function h(x) is given by: h(x) = 3x + 10Substituting h(x) into g(x): Now we will substitute h(x) into g(x) to find (g@h)(x). The function g(x) is given by: g(x) = (8x - 1) / (x + 4) So, (g@h)(x) = g(h(x)) = g(3x + 10)Performing the substitution: We will now perform the substitution: (g@h)(x) = g(3x + 10) = (8(3x + 10) - 1) / ((3x + 10) + 4)Simplifying the expression: Next, we simplify the expression: (g@h)(x) = (24x + 80 - 1) / (3x + 14) (g@h)(x) = (24x + 79) / (3x + 14)

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

{:[g(x)=(8x-1)/(x+4)],[h(x)=3x+10]:}
Write
(g@h)(x) as an expression in terms of
x.

(g@h)(x)=

$\begin{array}{l} g(x)=\frac{8 x-1}{x+4} \\ h(x)=3 x+10 \end{array}$ $\newline$ Write $(g \circ h)(x)$ as an expression in terms of $x$ . $\newline$ $(g \circ h)(x)=$

View step-by-step help

Home

Math Problems

Algebra 2

Domain and range of absolute value functions: equations

Full solution

\begin{array}{l} g(x)=\frac{8 x-1}{x+4} \\ h(x)=3 x+10 \end{array}

\newline

Write

(g \circ h)(x)

as an expression in terms of

x

\newline

(g \circ h)(x)=

Understanding $(g@h)(x)$ : First, we need to understand what $(g@h)(x)$ means. The notation $(g@h)(x)$ represents the composition of the functions $g$ and $h$ , which means we need to substitute the output of $h(x)$ into the function $g$ . So, we will first find $h(x)$ and then substitute it into $g(x)$ .
Finding $h(x)$ : Let's find $h(x)$ . The function $h(x)$ is given by: $\newline$ $h(x) = 3x + 10$
Substituting $h(x)$ into $g(x)$ : Now we will substitute $h(x)$ into $g(x)$ to find $(g@h)(x)$ . The function $g(x)$ is given by: $\newline$ $g(x) = \frac{8x - 1}{x + 4}$ $\newline$ So, $(g@h)(x) = g(h(x)) = g(3x + 10)$
Performing the substitution: We will now perform the substitution: $\newline$ $(g@h)(x) = g(3x + 10) = \frac{8(3x + 10) - 1}{(3x + 10) + 4}$
Simplifying the expression: Next, we simplify the expression: $\newline$ $(g@h)(x) = \frac{24x + 80 - 1}{3x + 14}$ $\newline$ $(g@h)(x) = \frac{24x + 79}{3x + 14}$