Given g of x is equal to

8x plus 2, find g of zero, g of negative 5,

and g 2x plus 3. So all this is, when they say

g of x is equal to 8x plus 2, this is a function definition. They’re saying

you give me any x, and you input it

into my function g, and my function g will output,

will associate with that number x, another number that

happens to be 8x plus 2. This is one way to

create an association. It’s going to associate

if you were to put 1 here. If this x is 1, you’re going

to do 8 times 1 plus 2. So you would

associate 1 through g. You’d associate 1 with 8

times 1 plus 2, which is 10. So it’s just another way

of creating association that you could do with

sets of ordered pairs or you could do it graphically. But this is one of

the most typical ways you’ll see a function defined. It says, look,

input an x over here and I’m going to

output 8x plus 2. So with that out of

the way, let’s think about what the g of 0 is. g of 0 literally

just means we’re inputting 0 into this function. And this function says,

whatever your inputting, I’m going to output

8 times that plus 2. So g of 0 is going to be–

let me write it this way so it becomes clear

what I’m doing. g of 0 is going to be 8

times is 0 plus 2. So wherever we saw the

x, we replaced it what it with whatever we’re inputting. That is our x in this

situation right over here. And so this is equal

to 8 times the 0 plus 2 is just equal to 2. So g of 0 is equal to 2. Let me just write that

here. g of 0 is equal to 2. Now let’s try g of negative 5. So let me write it this way. I’ll write it, g of

negative 5 is equal to– I’ll try to do the

color-coding a little bit better this time. It’s going to be equal

to 8 times our x, which in this case, is negative 5. 8 times negative 5 plus 2. We’re inputting x– We’re

inputting a negative 5. And we’re going to output

8 times negative 5 plus 2. Wherever we saw the x, we just

replace it with a negative 5. And this is just

equal to 8 times negative 5 is negative 40 plus

2 is equal to negative 38. So I’ll write this

over here on the right. We have g of negative 5

is equal to negative 38. Now, this last one is a

little bit interesting. So we just did this one. Now, let’s do g of 2x plus 3. So now they’re not

inputting a number. They’re inputting an expression. Now, what we have to do is

everywhere where we see x here, we’re going to replace

it with that expression. If I did g of a circle–

let me write this down. If I did g of an orange

circle right over here. By this function

definition, if I’m in putting an orange

circle, I should output an orange circle 8

times the orange circle, which doesn’t make

a lot of sense. But hopefully you get the idea

that whatever you’re inputting, you’re just going to multiply

it times 8 and add two. So if we input 2x plus 3, we’re

going to output this times 8 plus 2. Wherever we see an x, we replace

it with this right over here. So let’s try that out. So now we have g of 2x plus 3

is going to be equal to 8 times whatever we’re

inputting, eight times whatever inputting plus 2. If this was an orange,

we’d put an orange here. If this is a negative 5,

we put a negative 5 here. If this is a 0, we

put a zero here. In this case, we’re inputting

2x plus 3 into our function. So we put 2x plus 3 where

x is right over there. So 2x plus 3. Whatever we input, this function

says multiply by 8 and add 2. We’re inputting 2x plus

3, multiply it by 8, and then add 2. And so this is going to be equal

to– we just distribute the 8. And you get 16x plus 24. And then you still have

this plus 2 out over here So this is going to be

equal to 16x plus these two. You add them up, you get 26. So we can write

over here, and I’ll do that same color so

it can be consistent. We have g of 2x plus 3

is equal to 16x plus 26. And we’re done. I know it’s going

to be confusing because you’re inputting–

you’re replacing x with something

that has x in it, but you really

should just view this as if this was an orange ball

or a star or even if this had y’s is it. Wherever you see an

x, you replace it with whatever you

are inputting it. In every instance, we

replace the x with 2x plus 3.