# math!

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.

1. 👍 0
2. 👎 0
3. 👁 72

## Similar Questions

1. ### Maths

you have to solve the following by finding the value of x and y. can u help please? x+3(x+1)=2x 1+3(x-1)=4 2x-2(x+1)=5x 2(3x-1)=3(x-1) 4(y-1)+3(y+2)=5(y-4) 3y+7+3(y-1)=2(2y+6) These are exercises in standard algebraic manipulation

asked by number 420 on April 22, 2007
2. ### Algebra

Solve S=a/(1-r) for r S = a/(1-r) Multiply both sides by 1-r S*(1-r) = [(1-r)*a]/(1-r) Simplify S*(1-r) = a Multiply terms on the left. S - S*r = a Subtract S from both sides. S-S*r - S = a - S Simplify -S*r = a - S Multiply both

asked by Sara on July 19, 2007
3. ### Algebra

89. Solve for x in the equation: 6/7x - 6 = -2 I posted this before, and this is the reply I got from someone: multiply both sides by 7 6x-42=-14 add 42 to each side 6x=28 x=14/3 But I don't get how this is done because to

asked by y912f on May 7, 2010
4. ### Algebra

Which of the following describes a correct method for solving the equation below? -7/2n + 5 = -16 1. add 5 to both sides, then divide both sides by 2/7 2. subtract 5 from both sides, then multiply both sides by -7/2 3. add -5 to

asked by Anon on December 15, 2015
5. ### Pre-Algebra

inequality 0.75x>3 Multiply both sides of the inequality by 4/3 if you want to know what x is. from where did you get 4/3 to multiply to find x. How do you know that? MULTIPLY BOTH SIDES BY 4/3 The 4/3 comes from dividing both

asked by Amber :) on November 28, 2006

Help to solve this 1/2 (3g-2) = g/6 nevermind I was missing a bracket in the solution. multiply both sides by 2 This gives 3g-2=g/3 now cross multiply to get 9g-6=g now add a -g to both sides and +6 to both sides. g=3/4

asked by Confused on October 24, 2006
7. ### Another Problem...PLz Help COunt Iblis

Statements Reasons 1. 3x - 7 = -4 2. 3x - 7 + 7 = -4 + 7 3. 3x + 0 = -4 + 7 4. 3x + 0 = 3 5. 3x = 3 6. (1/3) 3x = 3 (1/3) 7. (1/3) 3x = 1 8. 1x = 1 9. x = 1 Is this problem about explaining each step? yeah like you have to write

asked by Margie... on December 2, 2006
8. ### Algebra

Solve each literal equations for the indicated variable D = C - s/n ( for s) s/n = D - C Next, multiply both sides of the above equation by n, to get the equation for s. i don't understand could you type it how it looks This is an

asked by Tammy Evert on July 8, 2006
9. ### Math, rational inequalities

Please can someone help me solve this problem? 2/x + 6/x-1 less than or = -5 8/x -1 = -4x Divide both sides by 4 2 >= -x Multiply both sides by -1 -2

asked by agirl on November 26, 2006
10. ### math

x/2=3y/5 can you show me how you got the answer please y=3/4x-2 I don't think it is correct. Starting over To solve for y first multiply both sides by 5 (5)x/2=3y/5 (5) Cancel 5 on right side to get 5x/2=3y Now multiply both sides

asked by Angel on July 7, 2005

More Similar Questions