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:

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

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))=

5x/(x+3)

The denominator is:(2(x+3)-(2x+1))/(x+3)=

5/(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

## Related Questions

- Another Problem...PLz Help COunt Iblis - Statements Reasons 1. 3x - 7 = -4 2. 3x...
- pre-algebra - x+5/4=3/4x The next step would be obtained by subtracting 3/4 x + ...
- Algebra - Solve Q= (N-S)/ N for N So when I multiply both sides by N I get Q(N...
- math - Next step, multiply both sides by (.01-x) .012(.01-x)=.01x+x^2 is the ...
- Maths - you have to solve the following by finding the value of x and y. can u ...
- math help1 - Okay I am a little bit confused about one math question can you ...
- algebra - Solve Q=(n-s)/n for n To get you started, multiply both sides by n and...
- math-inequalities - I really don't understand this stuff for example: 9b-3b+34&...
- Algebra - Solve each literal equations for the indicated variable D = C - s/n ( ...
- algebra - I need a step by step explanation on how to add these two equations 2x...