Determine inverse

1. Dec 15, 2004

aisha

1/(-3y+9) x cannot = 3 is the inverse y=(x+1/9)/(1/-3)? The 1 in the numerator is confusing me also how will I know if the inverse is a function?

2. Dec 15, 2004

learningphysics

That doesn't look right. When you find the inverse, you can check that you did it right by evaluating f-1(f(x)). It should come out to x. If it doesn't, that means your inverse is wrong.

3. Dec 16, 2004

delton

There are two easy ways to check.
Are the graphs of those functions symetrical about y=x? If so they are inverses.
AND EVEN EASIER
An inverse should have the x and y values of the original function switched.
Thats how one finds inverses: by switching x with y and solving for y.

4. Dec 16, 2004

HallsofIvy

Staff Emeritus
I'm not sure what you mean by y=(x+1/9)/(1/-3). Is that "x plus 1/9 divided by -1/3? If so, then it is easier to write it as -3(x+ 1/9)= -3x- 1/3.
If so, then, for example, if x= 1, then y= -3(1)- 1/3)= -3- 1/3= -10/3. And then
1/(-3((-10/3)+9) = 1/(10+9)= 1/19, not 1. So the two functions are certainly NOT inverse to one another.

What you do to find the inverse of a function like this is to "swap" x and y.
Your original function is y= -3x- 1/3. To find the inverse, swap x and y:
x= -3y- 1/3. Now solve for y: x+ 1/3= -3y so y= (-1/3)x- 1/9. Notice the negative signs!!!

5. Dec 17, 2004

aisha

I know how to find the inverse but the 1 in the numerator is confusing me, I dont know how to solve for y after switching x and y. f(x)=1/(-3y+9) how do i get rid of the numerator? Also since the denominator can be factored should I, or do i not have to?

6. Dec 18, 2004

t_unit92003

first of all, it should be x=1/(-3y+9). Then you solve for y by multiplying both sides by (-3y+9). then divide by x. then subtract 9 from both sides and divide both sides by -3. you should get y=(-3/x)-9.

7. Dec 20, 2004

aisha

I did all of that and I understand it well, but my answer is y=(x-9)/-3 or -3(x-9) how is the answer (-3/x)-9? :uhh: :uhh:

8. Dec 20, 2004

HallsofIvy

Staff Emeritus
How can you do "all of that" and "understand it well" and not know whether the answer is (x-9)/(-3) or -3(x-9)???

Your original function was y= 1/(-3x+ 9). Swapping x and y gives x= 1/(-3y+ 9)

That is the same as x(-3y+9)= 1 or, as t unit92003 said, -3y+ 9= 1/x. Subtracting 9 from both sides gives -3y= 1/x- 9 so y= (1/x- 9)/(-3)= 3- 1/(3x), not the (-3/x)- 9 that t unit92003 then gave.

9. Dec 22, 2004

aisha

I GOT UP TO THE LAST STEP, y=(1/x-9)/-3 Can someone please tell me how this became 3-1/(3x)? This is the only part im stuck on now plz help me understand this please....

10. Dec 22, 2004

HallsofIvy

Staff Emeritus
You did the algebra correctly but couldn't do the arithmetic??

(1/x- 9)/(-3)= (1/x)/(-3)- 9/(-3) by the "distributive property".

(1/x)/(-3)= -1/(3x) and -9/(-3)= 3.

(1/x- 9)/(-3)= (1/x)/(-3)- 9/(-3)= -1/(3x)+ 3= 3- 1/(3x).

11. Dec 25, 2004

aisha

THANKS FINALLY AFTER A LONG TIME OF TRYING I GOT IT!!! I had another question like that and was able to solve it thanks again everyone, esp Mentor.