Question

f(x)=3x-7 and g(x)=-2x-6 Find (f o g)(4)

Answer 1

f o g (x) = 3(2x-6)-7
Can you simplify?

Answer 2

No, I need a step by step explanation

Answer 3

So, composite functions are when you plug in a function for all the variables in another function. Do you see how I plugged it in?

Answer 4

Yes, sort of

Answer 5

I plugged in g(x) for every x in f(x).

Answer 6

Then you can either simplify or plug in 4 for x in the new function.

Answer 7

f o g(4) = 3(2*4-6) - 7

Answer 8

So that would be f o g(4)=-1
right?

Answer 9

Yup, good job! :)

Answer 10

Is that it? So all I need to do is put g(x) in for x in f(x), then substitute 4 for x?

Answer 11

You got it! Just remember that when there are multiple x's in f(x), to plug in g(x) for all of them.

Answer 12

Thanks, can you help me with a couple more?

Answer 13

Sure, but in 2 mins.

Answer 14

Thank you!!

What is the inverse of the given relation?
y = 3x + 12

Answer 15

Ok, inverse means switch x and y, then solve for x again.

Answer 16

So the first step is x = 3y + 12

Answer 17

Then solve for y.

Answer 18

Can you do that part?

Answer 19

You have to get y by itself, so you have to subtract 3 from both sides, right? So it would be x=y+9

Answer 20

You do want to get y by itself, but subtracting 3 from both sides wouldn't do that. Subtracting 3 from both sides would make
x -3 = 3y + 9

Answer 21

I would suggest first subtracting 12 from both sides to give
x - 12= 3y

Answer 22

Then dividing both sides by 3 to give
x/3 - 4 = y

Answer 23

But how do I solve the other side?

Answer 24

You can write it the other way. It's the same thing. Is that what you mean

Answer 25

?

Answer 26

Like y = x/3 - 4

Answer 27

That's what I thought, but I second guessed myself

Answer 28

Yup :)