Inverse Function.... please help me!!!!

G

Guest

Guest
Can someone plz help me find and explain the steps to find the inverse of:

f(x) = ( x-2 ) / ( 2x+3 )



I need the f -1 (x)
 
The general process is as follows:

. . . . .1) Rename "f(x)" as "y".
. . . . .2) Solve for "x=".
. . . . .3) Switch "x" and "y".
. . . . .4) Rename the new "y" as "f<sup>-1</sup>(x)".

So:

. . . . .f(x) = (x - 2)/(2x + 3)
. . . . .y = (x - 2)/(2x + 3)
. . . . .2xy + 3y = x - 2

...and so forth.

Eliz.
 
yes i understand all that, but this is where i am stuck....

(2x+3)x=y-2

I do not know how to finish the problem from here..... I need to get y= to something but i can't
 
You have a typo in your equation, I think. Please review the correct form, posted in my previous reply. Then get all the x-terms together on one side, factor out the "x", and divide off everything else.

Then continue through the posted steps.

Eliz.
 
ohh sorry i was taught to do these steps:

1. rewrite f(x) = as y=
2. switch x with y
3. solve for y
4. replace y with f-1(x)

so I went like this...

1. y=(x-2)/(2x+3)

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

3. this is where I am stuck.... I moved the 2y+3 to the left side and got:

(2y+3)x=y-2

and this is where i am stuck
 
It doesn't matter if you solve first and then switch, or switch first and then solve. The steps are still as I said: multiply things out (as I demonstrated), get all the terms containing the variable you're solving for together on one side; factor that variable out; and divide through by whatever is left on that side. This will leave you with your desired variable isolated on that side of the equation, with the inverse expression on the other side of the "equals" sign.

Eliz.
 
ahhh this problem is stressing me out!!!

ok so here is what you left me with

2xy + 3y = x - 2

how can I factor anything out of that....
 
You're skipping over the next step:

Isolate the terms that contain "y". That is, get them all together on one side of the equation.

Only then do you factor out the "y".

Then you divide off everything else from that side of the equation, leaving just "y=" on that side.

Eliz.
 
ok I think i got it.... sorry to be mean but I just sometimes do not understand math at all and I get very Frustrated..... so this is the answer I came up with, can you tell me if its right?


the inverse = (-3x-2) / (2x-1)
 
Yes, but don't be surprised if, for "neatness" or whatever, the book goes a step further:

. . .y = (-2 - 3x)/(1 - 2x)

. . . . .= [-1(3x + 2)] / [-1(2x - 1)]

. . . . .= (3x + 2)/(2x - 1)

Eliz.
 
You must log in or register to reply here.
Top