# Given f(n)=n-4 and g(n)=2n, how do you find 3f(n)+5g(n)?

Oct 26, 2016

$3 f \left(n\right) + 5 g \left(n\right) = 13 n - 12$

#### Explanation:

$f \left(n\right) = n - 4. \ldots \ldots \ldots \ldots \left(i\right)$
$g \left(n\right) = 2 n \ldots \ldots \ldots \ldots \ldots \ldots \left(i i\right)$

To find out: $3 f \left(n\right) + 5 g \left(n\right)$

Multiply $\left(i\right)$ by $3$.
$3 f \left(n\right) = 3 \left(n - 4\right)$
$\implies 3 f \left(n\right) = 3 n - 12. \ldots \ldots \ldots \ldots \ldots \ldots \left(i i i\right)$

Multiply $\left(i i\right)$ by $5$.
$5 g \left(n\right) = 5 \left(2 n\right)$
$\implies 5 g \left(n\right) = 10 n \ldots \ldots \ldots \ldots \ldots \ldots \ldots . \left(i v\right)$

Now, Add $\left(i i i\right)$ and $\left(i v\right)$

$\implies 3 f \left(n\right) + 5 g \left(n\right) = 3 n - 12 + 10 n$
$\implies 3 f \left(n\right) + 5 g \left(n\right) = 13 n - 12$