Question

WILL GIVE MEDAL!!!!

Given the following functions f(x) and g(x), solve f[g(6)] and select the correct answer below:
f(x) = 6x + 12
g(x) = x − 8

A: -96
B: 0
C: 24
D: 48

Answer 1

The notation might be getting you confused. If I want g(10) that means, look at the definition of g(x) and replace all the x's with 10. So we have g(10) = 10 - 8 = 2

Answer 2

Solve that?

Answer 3

Same thing with f. We can go nuts with this and do f( g(10) ). Don't freak out! This just means:

First find out what g(10) is. We found it to be 2. Now we can just do f(2).

Answer 4

f(2)=10-8=2 ?

Answer 5

Exactly right

Answer 6

Wait no

Answer 7

I think you might be having trouble understanding functions. Do you know what it means to square a number?

Answer 8

Yes I do

Answer 9

Ok cool. Let's do an example with that.

Answer 10

Okayyy

Answer 11

To square a number, you just times it by itself.

I can describe this mathematically as a function:
square(x) = x * x

This says I have a function called "square", it takes in a number - and for the purposes of referring to this number, we call it x. In order to calculate the output of our square function, we multiply x by itself.

So now how do we use it? Let's say I want to calculate 5 squared. I can use my square function!

Let's feed it 5.
So we write square(5)

Now to calculate it, I look at what's inside the brackets, and it is 5. So x is now 5. To calculate the output, it's x*x, or with my input, it's just 5*5. We end up with

square(5) = 25

Answer 12

Your f and g functions are a bit more abstract than this. It's not quite apparent what they might be used for. But that's not a problem. We can treat them exactly like we did the square function.

Answer 13

Wait go back to the actual problem. the first would be 72 and the second is 2 @cardboardbox

Answer 14

If by first you mean f(10) and second you mean g(10) then yes

Answer 15

Yes that's what I meant

Answer 16

What do I do next?

Answer 17

Say we have another function "cube" which multiplies a number by itself and then again once more.

You may (for reasons unknown) want to find the square of 3 cubed. We can write this as

square( cube(3) ).

So first we figure out what cube(3) is, and finally we can square that number to get our result.

Answer 18

Confused again

Answer 19

What do I have to cube

Answer 20

Cube(3) means 3*3*3 which is 27

Answer 21

In my example I am cubing 3, then squaring the result

Answer 22

So square( cube(3) ) means, first figure out cube(3), which turns out to be 27. Then square 27 to get 729.

Answer 23

Is c the answer?

Answer 24

How did you arrive at that

Answer 25

Or do you subtract everything from 729?

Answer 26

729 was just my example

Answer 27

Oh, but I need to do the original problem @cardboardbox