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Given that
f(x)=3x,quad g(x)=x+2 and
h(x)=-3f(x-2)+2g(x+2), then what is the value of
h(3) ?
Answer:

Given that $f(x)=3 x, \quad g(x)=x+2$ and $h(x)=-3 f(x-2)+2 g(x+2)$ , then what is the value of $h(3)$ ? $\newline$ Answer:

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Solve equations with variables on both sides

Full solution

Q. Given that

f(x)=3 x, \quad g(x)=x+2

and

h(x)=-3 f(x-2)+2 g(x+2)

, then what is the value of

h(3)

?

\newline

Answer:

Find $f(3)$ : First, we need to find the value of $f(x)$ when $x$ is replaced by $3$ . $\newline$ $f(x) = 3x$ $\newline$ $f(3) = 3(3)$ $\newline$ $f(3) = 9$
Find $g(3)$ : Next, we need to find the value of $g(x)$ when $x$ is replaced by $3$ .
$g(x) = x + 2$
$g(3) = 3 + 2$
$g(3) = 5$
Find $f(1)$ : Now, we need to find the value of $f(x-2)$ when $x$ is replaced by $3$ .
$f(x-2) = 3(x-2)$
$f(3-2) = 3(3-2)$
$f(1) = 3(1)$
$f(1) = 3$
Find $g(5)$ : We also need to find the value of $g(x+2)$ when $x$ is replaced by $3$ .
$g(x+2) = (x+2) + 2$
$g(3+2) = (3+2) + 2$
$g(5) = 5 + 2$
$g(5) = 7$
Calculate $h(3)$ : Now we can calculate $h(x)$ using the values of $f(x-2)$ and $g(x+2)$ we found. $\newline$ $h(x) = -3f(x-2) + 2g(x+2)$ $\newline$ $h(3) = -3f(1) + 2g(5)$ $\newline$ $h(3) = -3(3) + 2(7)$ $\newline$ $h(3) = -9 + 14$ $\newline$ $h(3) = 5$

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