SOLUTION: I am stuck on this problem. If I can see this worked out it would help a lot! If f(x) = (1/x - 9x) / (1+3x), what is f(1/x). My book says the answer is x-3 but I cannot get

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Question 1010711: I am stuck on this problem. If I can see this worked out it would help a lot!
If f(x) = (1/x - 9x) / (1+3x), what is f(1/x).
My book says the answer is x-3 but I cannot get this same answer.
Found 4 solutions by It is costly, Theo, rothauserc, MathTherapy:
Answer by It is costly(175)   (Show Source): You can put this solution on YOUR website!

Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
problem is:

f(x) =

what is f(1/x)

you replace x with 1/x and the equation becomes:

f(x) =

1/(1/x) = 1*x = x
9*1/x = 9/x
3*(1/x) = 3/x

equation becomes:

f(1/x) =

multiply numerator and denominator of this equation by x to get:

f(1/x) =

x^2 - 9 = (x-3) * (x+3)

equation becomes:

f(1/x) =

the x+3 in the numerator and in the denominator cancel out and you are left with:

f(1/x) = (x-3)





Answer by rothauserc(4718)   (Show Source): You can put this solution on YOUR website!
If f(x) = (1/x - 9x) / (1+3x), what is f(1/x).
f(1/x) = ((1/(1/x))-9(1/x)) / (1+3(1/x)) =
(x - (9/x)) / (1 + 3(1/x)) =
((x^2-9) / x) / ((x+3) / x)) =
(((x+3)(x-3)) / x) * (x / (x+3)) =
(x-3)
Answer by MathTherapy(10556)   (Show Source): You can put this solution on YOUR website!

I am stuck on this problem. If I can see this worked out it would help a lot!
If f(x) = (1/x - 9x) / (1+3x), what is f(1/x).
My book says the answer is x-3 but I cannot get this same answer.










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