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Given that
f(x)=x-5,quad g(x)=-5x and
h(x)=-3f(x)+3g(x+2), then what is the value of
h(6) ?
Answer:

Given that $f(x)=x-5, \quad g(x)=-5 x$ and $h(x)=-3 f(x)+3 g(x+2)$ , then what is the value of $h(6)$ ? $\newline$ Answer:

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Evaluate expression when a complex numbers and a variable term is given

Full solution

Q. Given that

f(x)=x-5, \quad g(x)=-5 x

and

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

, then what is the value of

h(6)

?

\newline

Answer:

Calculate $f(6)$ : Given the functions: $\newline$ $f(x) = x - 5$ $\newline$ $g(x) = -5x$ $\newline$ We need to find $h(x) = -3f(x) + 3g(x + 2)$ and then evaluate $h(6)$ . $\newline$ First, let's find $f(6)$ and $g(6 + 2)$ separately. $\newline$ $f(6) = 6 - 5$
Calculate $g(6 + 2)$ : Now we calculate $f(6)$ : $\newline$ $f(6) = 6 - 5$ $\newline$ $f(6) = 1$
Substitute values into $h(x)$ : Next, we calculate $g(6 + 2)$ :
$g(6 + 2) = g(8)$
$g(8) = -5 \times 8$
$g(8) = -40$
Calculate $h(6)$ : Now we have $f(6)$ and $g(8)$ , we can substitute these values into $h(x)$ :
$h(x) = -3f(x) + 3g(x + 2)$
$h(6) = -3f(6) + 3g(8)$
$h(6) = -3 \times 1 + 3 \times (-40)$
Calculate $h(6)$ : Now we have $f(6)$ and $g(8)$ , we can substitute these values into $h(x)$ :
$h(x) = -3f(x) + 3g(x + 2)$
$h(6) = -3f(6) + 3g(8)$
$h(6) = -3 \times 1 + 3 \times (-40)$ Finally, we calculate $h(6)$ :
$h(6) = -3 \times 1 + 3 \times (-40)$
$h(6) = -3 - 120$
$f(6)$ $0$

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