Question

find the inverse of the function (in comments)

Answer 1

\[f(n)=\frac{ -n+5 }{ 2 }\]

Answer 2

greatly would appreciate your help on this one @jim_thompson5910

Answer 3

i know i switch x and y

Answer 4

the first thing to do is to substitute f(n) for y

Answer 5

then switch n and y

Answer 6

then solve for y

Answer 7

care to show me the steps of solving for y

Answer 8

you get this part right \[\huge n = \frac{-y+5}2\]

Answer 9

?

Answer 10

yes

Answer 11

What you want to accomplish is y on one side of the equation and everything else on the other. A good first step is to get rid of that denominator 2. How would you do that?

Answer 12

multiply it so \[2x=-y+5\]

Answer 13

That's right. Could you work your way from here? Remember, your goal is to isolate y (make sure y is one side of the equation)

NOTE: I mean y, not -y ;)

Answer 14

could you actually take me step by step, i am not quite sure that i understand what to do next.

Answer 15

Ok, we want to bring everything without y on the other side
You have
2n = -y + 5
(yes, it's n, not x ;) )
First, you'll want to get rid of that +5 that is next to the y, how would you do that?

Answer 16

subtract it

Answer 17

Please demonstrate :)

Answer 18

\[2x-5=-y\]
then you divide by -1
\[y=\frac{ 2x-5 }{ -1 }\]

Answer 19

Wow, that escalated quickly :D
You've done well, now, what happens when you divide by -1?

Answer 20

hahaha c: uhhm you dont do anything, do you?

Answer 21

Well, actually, when you got to
2x - 5 = -y
You divided both sides by -1, you could also multiply both sides by -1, it has the same effect, but it's easier to see the result.

Just to be clear:
\[\frac{k}{-1}=k \left( \frac{1}{-1} \right)=k \left( \frac{-1}{1} \right)=\frac{-k}{1}=-k\]

Answer 22

That said, now what can you say about
\[y=\frac{ 2x-5 }{ -1 }\]?

Answer 23

hmm still not sure

Answer 24

Remember what happened to k when it was divided by -1? Refer to that which I posted.

Answer 25

y=-2x-5 ?

Answer 26

Please reconsider... :)

Answer 27

y=-2x+5

Answer 28

Yeah, sort of, just replace x with n

Answer 29

nope that's not it either

Answer 30

Of course that's not it, you started with n, you can't end up with x :P

Answer 31

it still isn't correct if it is n. if you plug in numbers for the variables, it doesn't appear to be the inverse

Answer 32

invof f=5-2x

Answer 33

How do you know? Can you give an example?

Answer 34

solve for n

Answer 35

You ended up with -2n + 5
Let's call that g(n)

For a function f,
g would be its inverse if
f(g(n)) = n
could you try that now?

Answer 36

2f=-n
2f-5=-n
5-2f=n

Answer 37

2f=-n+5
2f-5=-n
5-2f=n
as n , are used for notations you can consider inverse of f(x)=5-2x