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

Algebra ->  Functions -> 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       Log On


   

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

f(x) = %281%2Fx+-+9x%29+%2F+%281+%2B+3x%29

what is f(1/x)

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

f(x) = %281%2F%281%2Fx%29+-+9%2A1%2Fx%29+%2F+%281+%2B+3%2A%281%2Fx%29%29

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

equation becomes:

f(1/x) = %28x-9%2Fx%29+%2F+%281+%2B+3%2Fx%29

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

f(1/x) = %28x%5E2-9%29+%2F+%28x+%2B+3%29

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

equation becomes:

f(1/x) = %28%28x%2B3%29%2A%28x-3%29%29+%2F+%28x%2B3%29

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) About Me  (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(10555) About Me  (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.
f%28x%29+=+%281%2Fx+-+9x%29%2F%281+%2B+3x%29

f%281%2Fx%29+=+%281%2F%281%2Fx%29+-+9%281%2Fx%29%29%29%22%F7%22%281+%2B+3%281%2Fx%29%29

f%281%2Fx%29+=+%281+%2A+%28x%2F1%29+-+9%2Fx%29%29%22%F7%22%281+%2B+3%2Fx%29

f%281%2Fx%29+=+%28x+-+9%2Fx%29%29%22%F7%22%281+%2B+3%2Fx%29

f%281%2Fx%29+=+%28%28x%5E2+-+9%29%2Fx%29%22%F7%22%28%28x+%2B+3%29%2Fx%29

f%281%2Fx%29+=+%28%28x+-+3%29%28x+%2B+3%29%2Fx%29%22%F7%22%28%28x+%2B+3%29%2Fx%29 ------ Factoring x%5E2+-+9

f%281%2Fx%29+=+%28%28x+-+3%29%28x+%2B+3%29%2Fx%29%22%2A%22%28x%2F%28x+%2B+3%29%29 ------ Applying KEEP, CHANGE, FLIP

f%281%2Fx%29+=+%28highlight%28%28x+-+3%29%29cross%28%28x+%2B+3%29%29%2Fcross%28x%29%29%22%2A%22%28cross%28x%29%2Fcross%28%28x+%2B+3%29%29%29

highlight_green%28f%281%2Fx%29+=+x+-+3%29