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Given that
f(x)=3x,g(x)=x+3 and
h(x)=2f(x+1)+3g(x), then what is the value of
h(6) ?
Answer:

Given that $f(x)=3 x, g(x)=x+3$ and $h(x)=2 f(x+1)+3 g(x)$ , then what is the value of $h(6)$ ? $\newline$ Answer:

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Write and solve direct variation equations

Full solution

Q. Given that

f(x)=3 x, g(x)=x+3

and

h(x)=2 f(x+1)+3 g(x)

, then what is the value of

h(6)

?

\newline

Answer:

Understand Given Functions: Understand the functions given and what is being asked. $\newline$ We are given three functions $f(x)$ , $g(x)$ , and $h(x)$ , and we need to find the value of $h(6)$ .
Calculate $f(7)$ : Calculate $f(6+1)$ since $h(x)$ involves $f(x+1)$ . $\newline$ $f(x) = 3x$ , so $f(6+1) = f(7) = 3 \times 7$ .
Calculate $g(6)$ : Calculate the value of $f(7)$ . $f(7) = 3 \times 7 = 21$ .
Calculate $h(6)$ : Calculate $g(6)$ since $h(x)$ involves $g(x)$ . $g(x) = x + 3$ , so $g(6) = 6 + 3$ .
Substitute Values for $h(6)$ : Calculate the value of $g(6)$ . $g(6) = 6 + 3 = 9$ .
Perform Calculations: Use the values of $f(7)$ and $g(6)$ to calculate $h(6)$ . $h(x) = 2f(x+1) + 3g(x)$ , so $h(6) = 2f(7) + 3g(6)$ .
Add Results for $h(6)$ : Substitute the values of $f(7)$ and $g(6)$ into the equation for $h(6)$ . $\newline$ $h(6) = 2 \times 21 + 3 \times 9.$
Add Results for $h(6)$ : Substitute the values of $f(7)$ and $g(6)$ into the equation for $h(6)$ .
$h(6) = 2 \times 21 + 3 \times 9$ . Perform the calculations.
$h(6) = 2 \times 21 + 3 \times 9 = 42 + 27$ .
Add Results for $h(6)$ : Substitute the values of $f(7)$ and $g(6)$ into the equation for $h(6)$ .
$h(6) = 2 \times 21 + 3 \times 9$ . Perform the calculations.
$h(6) = 2 \times 21 + 3 \times 9 = 42 + 27$ . Add the results to find $h(6)$ .
$h(6) = 42 + 27 = 69$ .

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