g(x)=3x-5 h(x)=(2)/(2x+3) Write h(g(x)) as an expression in terms of x. h(g(x))=

Substitute g(x) into h(x): First, we need to substitute the expression for g(x) into h(x) to find h(g(x)). The function g(x) is given as 3x-5, so we will replace every x in h(x) with 3x-5.Simplify h(g(x)) expression: The function h(x) is (2)/(2x+3). Substituting g(x) into h(x), we get h(g(x)) = (2)/(2(3x-5)+3).Simplify expression inside parentheses: Now, we simplify the expression inside the parentheses: 2(3x-5)+3 = 6x - 10 + 3.Further simplification: Simplifying further, we get 6x - 10 + 3 = 6x - 7.Write complete expression for h(g(x)): Now, we can write the complete expression for h(g(x)): h(g(x)) = (2)/(6x - 7).

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g(x)=3x-5

h(x)=(2)/(2x+3)
Write
h(g(x)) as an expression in terms of
x.

h(g(x))=

$g(x)=3 x-5$ $\newline$ $h(x)=\frac{2}{2 x+3}$ $\newline$ Write $h(g(x))$ as an expression in terms of $x$ . $\newline$ $h(g(x))=$

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Math Problems

Algebra 1

Find the inverse of a linear function

Full solution

g(x)=3 x-5

\newline

h(x)=\frac{2}{2 x+3}

\newline

Write

h(g(x))

as an expression in terms of

x

\newline

h(g(x))=

Substitute $g(x)$ into $h(x)$ : First, we need to substitute the expression for $g(x)$ into $h(x)$ to find $h(g(x))$ . The function $g(x)$ is given as $3x-5$ , so we will replace every $x$ in $h(x)$ with $3x-5$ .
Simplify $h(g(x))$ expression: The function $h(x)$ is $\frac{2}{2x+3}$ . Substituting $g(x)$ into $h(x)$ , we get $h(g(x)) = \frac{2}{2(3x-5)+3}$ .
Simplify expression inside parentheses: Now, we simplify the expression inside the parentheses: $2(3x-5)+3 = 6x - 10 + 3$ .
Further simplification: Simplifying further, we get $6x - 10 + 3 = 6x - 7$ .
Write complete expression for $h(g(x))$ : Now, we can write the complete expression for $h(g(x))$ : $h(g(x)) = \frac{2}{6x - 7}$ .