Question

Find the inverse of f
a.) 2x/x+7
b.) 4x/3x-7

Answer 1

@jim_thompson5910 Could you help me with problem please?

Answer 2

a) is

\[\Large f(x) = \frac{2x}{x+7}\]

right?

Answer 3

@jim_thompson5910 it says that's wrong...

Answer 4

what did you get?

Answer 5

i didn't get anything cause i didn't know how to approach the problem?

Answer 6

but you said "it says that's wrong..."

that implies you got an answer of some kind

Answer 7

oh sorry i'm stupid

Answer 8

yes you were right with \[\frac{ 2x}{ x+7 }\]

Answer 9

so what you need to do is solve for y

\[\Large x=\frac{2y}{y+7}\]

Answer 10

ok so what do i do from there?

Answer 11

did you solve for y?

Answer 12

i didn't know hwo to sorry

Answer 13

it might help to multiply both sides by y+7 first

Answer 14

then you'd get...
x(x+7)=2y
xy+7x=2y

Answer 15

good

Answer 16

why not get all the y terms to one side

Answer 17

so move the xy over

Answer 18

and try to isolate y

Answer 19

wait what? sorry...

Answer 20

xy+7x=2y

7x=2y-xy ... Subtract xy from both sides.

Answer 21

the goal is to isolate y

Answer 22

oh okay

Answer 23

that would make it
7x=y(2-x)

Answer 24

yes

Answer 25

you have one more step

Answer 26

divide both sides by y?

Answer 27

and subtract 7x from both sides?

Answer 28

if you divided both sides by y, you'd just get y back onto a side with other terms

you want to get y all by itself

Answer 29

how do you do that?

Answer 30

give it a shot, try to get y all by itself

7x = y*(2-x)

Answer 31

try to move that 2-x over

Answer 32

6x+2=y?

Answer 33

wait that won't work

Answer 34

the only wait to move the (2-x) is to divide it to both sides right?

Answer 35

correct

Answer 36

divide both sides by 2-x

Answer 37

so the final answer would be 7x/ (2-x)

Answer 38

yes

Answer 39

thankyou!! & I tried to do part b by myself this time and I got ...
y=-7x/(4-3x) and it says it's wrong, but i don't know what i did wrong

Answer 40

x = 4y/(3y-7)

x(3y-7) = 4y

3xy - 7x = 4y

I'll let you finish

Answer 41

would 3xy-7x=4y would go to be x(3y-7)=4y

Answer 42

but wiat that wouldn't work

Answer 43

move the y term over

Answer 44

get all the y terms together

Answer 45

so...
-4y+3xy-7x=0?

Answer 46

move the 7x over so the y terms are on their own side

Answer 47

ok that makes sense

Answer 48

wait but where would the 3xy be?

Answer 49

you would have -4y+3xy = 7x

Answer 50

alright thanks I got it!!

Answer 51

np