Question

Are f and g inverses of each other?

Answer 1

f(x)=-24x+9; g(x)=(x-9)/-24

Answer 2

so, in order to be an inverse, what has to happen?

Answer 3

Don't you invert the function with respect to a given variable

Answer 4

f(g(x))=?
and g(f(x))=?

Answer 5

it's easier than that, although that is one way

Answer 6

by inverts you mean switch x and y, i guess?

Answer 7

I always though that you just have to change the + to a - like this -24x-9?

Answer 8

oh, no, that is not it

Answer 9

so the inverse is a function that "undoes" the initial function

Answer 10

so by definition, f(g(x))=g(f(x))=x, if the functions are inverses

Answer 11

for example, let's find the inverse of f(x)=2-x

Answer 12

well, f(x)=y, so
y=2-x

Now, our inverting step is to switch the variables

x=2-y

Solving for y,
x-2=-y
y=-x+2 or 2-x.

Now it appears that this function is its own inverse. Let's check

f(g(x))=2-(2-x)

solving we get
f(g(x))=2-2+x
f(g(x))=x
So, since it equals what we put in, x, these are indeed inverses

Answer 13

So, try this on your problem \[f(x)=-24x+9; ~~g(x)=\frac{x-9}{-24}\]

Answer 14

So to start would the first step look like x = - 24 y + 9?

Answer 15

you can do it that way. Or you could skip the solve for the inverse step and just see if f(g(x))=x

Answer 16

so whenever you solve what you have written for y, you should get g(x) if it is an inverse

Answer 17

Would that be 9-x/24

Answer 18

I wouldn't distribute the negative since they didn't for g, but pretty much

Answer 19

inverse of -24x+9 is 9-x/24?

Answer 20

which is the same as their g(x) if you pull a minus 1 out of the top

Answer 21

So that would mean that the answer is no they are not inverses?

Answer 22

no, they are because they are the same. What you got and g(x) are the same thing

Answer 23

now, you can just plug the two into each other to check if you are not convinced

Answer 24

oh I see because g(x)=(x-9)/-24 the inverse of that would be 9-x/24 so they are inverses.

Answer 25

no no, those are the same equations

Answer 26

Oh I see now so when I plug them into each other I will see that they are inverses?

Answer 27

inverse has nothing to do with changing +/- signs. Thats conjugate

Answer 28

when you plug g(x) into f(x) you will

Answer 29

ok thank you very much for your time and help :)

Answer 30

np, please check by plug and chugging g into f. That's the easier way to begin with.

Answer 31

ok I going to

Answer 32

how did you get there? that is how you think of inverses

2+1 = 3

how did you get to 3
usually the parts and pieces in the equation gives you a hint how.