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Find f^-1 in similar form for each of the following functions.
Question no. 1 ↓
f:x→3x over x-3,x not equal to 3
Question no. 2 ↓
f:x→2x+4 over 2x-1,x not equal to 1over2

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asked by mandy
  1. I will do the 2nd, you do the 1st in the same way

    f(x) = (2x+4)/(2x-1)
    or
    y = (2x+4)/(2x-1)
    inverse by switching x's and y's
    x = (2y+4)/(2y-1)
    simplify and solve this for y ....
    2xy - x = 2y+4
    2xy - 2y = x+4
    y(2x - 2) = x+4
    y = (x+4)/(2x-2)

    f^-1 (x) = (x+4)/(2x-2) , x ≠ 1

    I usually test my answer, let x = 3 , (I get no fractions)
    f(3) = 10/5 = 2
    f^-1 (2) = 6/2 = 3

    (this does not "prove" that my answer is right, but if I did not get 3 as my return answer, by equation would have been wrong. My test "strongly suggests" that I am right)

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    posted by Reiny
  2. Reiny,thanks a lot! You are right...can you explain why the answer x is not equal to 1 ?

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    posted by mandy
  3. What would happen if you sub x = 1 into our new denominator?
    Can we divide by zero ?

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    posted by Reiny
  4. Ohh...ok..thank you!

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    posted by mandy
  5. No.1
    y=3x/x-3
    x=3y/y-3
    xy-3y=3x
    y(x-3)=3x
    y=3x/x-3
    f^-1(x)=3x/x-3,x≠3
    Am i correct ?:D

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    posted by mandy
  6. yes, but in this form of typing you have to use brackets.

    f^-1 (x) = 3x/(x-3) or else the 3x is divided by x only

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    posted by Reiny

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