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Given that
f(x)=x+4,quad g(x)=4x and
h(x)=2f(x-1)+3g(x), then what is the value of
h(1) ?
Answer:

Given that $f(x)=x+4, \quad g(x)=4 x$ and $h(x)=2 f(x-1)+3 g(x)$ , then what is the value of $h(1)$ ? $\newline$ Answer:

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Write and solve inverse variation equations

Full solution

Q. Given that

f(x)=x+4, \quad g(x)=4 x

and

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

, then what is the value of

h(1)

?

\newline

Answer:

Given Functions: Given the functions $f(x) = x + 4$ , $g(x) = 4x$ , and $h(x) = 2f(x - 1) + 3g(x)$ , we need to find the value of $h(1)$ . Let's start by finding the value of $f(x - 1)$ and $g(x)$ when $x = 1$ .
Calculate $f(0)$ : First, we calculate $f(1 - 1)$ which is $f(0)$ . Using the definition of $f(x)$ , we have $f(0) = 0 + 4 = 4$ .
Calculate $g(1)$ : Next, we calculate $g(1)$ using the definition of $g(x)$ . We have $g(1) = 4 \times 1 = 4$ .
Substitute into $h(1)$ : Now we have both $f(0)$ and $g(1)$ , we can substitute these values into the definition of $h(x)$ to find $h(1)$ . So, $h(1) = 2f(1 - 1) + 3g(1) = 2f(0) + 3g(1)$ .
Final Calculation: Substitute the values we found into the equation for $h(1)$ : $h(1) = 2 \times 4 + 3 \times 4 = 8 + 12 = 20$ .

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