Question

f(x) = (2x-3)/(x+4). find f^-1(x)

Answer 1

\[f^{-1}(x)\]?

Answer 2

yes

Answer 3

where r u stuck?

Answer 4

i know that u know the procedure

Answer 5

OK,\[y = f(x)\]\[y = {2x - 3 \over x +4}\]Plug in \(x\) with \(y\).\[x = {2y - 3 \over y + 4}\]Solve for \(x\).

Answer 6

well i worked it out and got a quadratic on one side.. so now i started over.

Answer 7

@ParthKohli if you plug in x with y .. would you then solve for y instead of x?

Answer 8

so after multiplying y+4 to both sides.. i get xy+4x = 2y-3 am i on the right track?

Answer 9

\(\huge x=\frac{2y+8-11}{y+4}=\frac{2(y+4)}{y+4}-\frac{11}{y+4}\)

Answer 10

=2-11/(y+4)
subtract 2 from both sides.

Answer 11

did u get that step ?

Answer 12

no

Answer 13

my paper is a mess now :( i got the inverse as x+5.. sigh

Answer 14

\[x=\frac{ 2y-3 }{y+4 }\]

Answer 15

then i multiply both sides by Y+4 to get

Answer 16

don't do that

Answer 17

xy+4x = 2y -3

Answer 18

okay

Answer 19

don't we just take the derivative and plug in 1?

Answer 20

i dont even know what that means :)

Answer 21

write -3 as 8-11
2y-3 = 2y+8-11
= 2(y+4) -11

Answer 22

i don't think u are getting this ^ @Nameless

Answer 23

i am trying to derive a way to do every problem like this.... thus if it is x = y-1/3x+5

Answer 24

then i simply replace x with y and solve for y. multiply both sides by 3y+5 then rearrange and factor out the y to get y(3x-1) = -5x-1 .. then divide 3x-1 by -5x-1 to get y = -5x-1/3x-1

Answer 25

i am trying to do it your way.. but its different than i have learned in class.. so

Answer 26

ok, u have
x= (2y-3) / (y+4)
x(y+4) = 2y-3

xy+4x = 2y-3
xy-2y+4x = -3

xy -2y =-3-4x
y(x-2) = -(3+4x)

y=-(3+4x)/ (x-2)

make sense ?

Answer 27

yes!

Answer 28

ask if any doubts in any step ...

Answer 29

the one u typed is the one i had been doing.. but got confused with the algebra... mostly what to move.. i see now, thank you so very much

Answer 30

welcome :)