April 17, 2014

Homework Help: math!

Posted by kristie on Thursday, July 20, 2006 at 1:31pm.

about finding the inverse of y=(2x+1)/(x+3).

should you multiply (x+3) on both sides and get y(x+3)=2x+1?
then what would be your next step?

This one is a little tricky because we we have a rational function.
What we want to end up with is x(y)
To do this you can interchange x and y and try to solve for x. That function is the inverse. Thus:
x=(2y+1)/(y+3), then solve for y
(y+3)x= (2y+1)
yx+3x = 2y+1
3x-1=2y-yx =
3x-1= y(2-x) =
y= (3x-1)/(2-x)
Now interchange the x and y again. (after isolating y)
y = (3x-1)/(2-x)

And if we did things correctly, we should have the inverse function. Test it by composing functions.
(3((2x+1)/(x+3) -1))/(2-(2x+1)/(x+3))=
The numerator is:((6x+3)-(x+3))/(x+3))=
The denominator is:(2(x+3)-(2x+1))/(x+3)=
Putting them together we have 5x/(x+3) times (x+3)/5 = x.
Thus they are inverses. Test it by graphing too.

That makes sense! Thank you so much!!!

comment:I don't think the second interchange is necessary if we want y(x). It's been awhile since I worked this, so check my work and ask questions if anything isn't clear.

Answer this Question

First Name:
School Subject:

Related Questions

Maths - you have to solve the following by finding the value of x and y. can u ...
math - hi, i need help with solving this equation for "y" 2x+3y=-2 2x+3y=-2 Get ...
Math - how would i do 2x+12=5x+8-x????????? 2x+12=5x+8-x This seems to be a ...
please help math - x/3-2/3=1/x *Solve the rational below. I really need help. ...
Pre Calculus - Solve 2cos^2(2x)=1 I divided both sides by 2 and got this cos^2(...
Maths - Can you please help explain how to get the answer to 3/x = 2/5 thanks a ...
algebra - I need a step by step explanation on how to add these two equations 2x...
algebra - I made a mistake in my problem . can you take me step by step on how ...
pre-algebra - x+5/4=3/4x The next step would be obtained by subtracting 3/4 x + ...
math - 2x+3y=6 (solve for x) 2x+3y=6 Get unknown on one side and everything else...