Determining the Inverse of 1/(-3y+9): x≠3

[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?

 

[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.

 

[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.

 

[HallsofIvy]

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!

 

[aisha]

I know how to find the inverse but the 1 in the numerator is confusing me, I don't 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?

 

[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.

 

[aisha]

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.

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?

 

[HallsofIvy]

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.

 

[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 I am stuck on now please help me understand this please...

 

[HallsofIvy]

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).

 

[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.