Question

Let g be the inverse of f. Find g(x)

Answer 1

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

Answer 2

to find the inverse of f you need first to find x in terms of y
let y = -x + 2 / (-2x + 2)

can you do that?

Answer 3

cross multiply:-
-2xy + 2y = - x + 2
x - 2xy = 2 -2y

can you continue?

Answer 4

factor the left hand side Take out x.

Answer 5

i think so yes

Answer 6

i dont understand

Answer 7

ok so what do you get?

Answer 8

i know that we have to find the inverse but i dont know how

Answer 9

x is common to x and 2xy so we can factor the left sides
x - 2xy = x(1 - 2y)

Answer 10

why is there 2xy?

Answer 11

this is what i am doing
you first replace f(x) by y ( i could have used any letter)
then find x in terms of y

Answer 12

so far we have
x(1 -2y) = 2 - 2y

now we have to isolate x

so how do we do that?

Answer 13

the came from the first step which was cross multiplying

Answer 14

* the 2xy came from