# How do you find g(3)-h(3) given g(x)=2x-5 and h(x)=4x+5?

Jun 11, 2018

$- 16$

#### Explanation:

A function is an associator rules, in this case between numbers. This means that a function receives an input, and gives a rule to compute the output, in terms of that inuput.

For example, if you define $g \left(x\right) = 2 x - 5$, it means that you're defining a function, named $g$, which works as follows: you give a certain number $x$ to $g$ as input, and it returns twice that number ($2 x$) minus five $- 5$.

This works for any number you can think of: if you give $10$ as input to $g$, it will return twice that number (so $20$) minus five (so $15$).

This means that when you write something like $g \left(3\right)$, you want to evaluate that function for that explicit input. You are asking: what happens if I give $3$ as input to $g$?

Well, $g$ behaves always in the same way: it will return twice the number you gave it, minus five.

In this case, the number we gave it is $3$, so the output will be $2 \cdot 3 - 5 = 6 - 5 = 1$

The same goes for $h$, except it is a different function, and thus follows different rules. So, since $h \left(x\right) = 4 x + 5$, the behaviour of $h$ will be returning four times the number you gave it, plus five.

Again, we want to compute $h \left(3\right)$, which means that the output is $4 \cdot 3 + 5 = 12 + 5 = 17$

Finally, we want to compute $g \left(3\right) - h \left(3\right)$, but we already computed both numbers, so we can translate

$g \left(3\right) - h \left(3\right) = 1 - 17 = - 16$