FUNCTIONS HELP!!! f(x)=x/x-1 find ff(x)?
回答 (3)
2011-03-06 9:28 pm
✔ 最佳答案
I am assuming you wish to find f[f(x)].With f(x) = x/(x - 1), we see that:
f[f(x)]
= f[x/(x - 1)], since f(x) = x/(x - 1)
= [x/(x - 1)]/[x/(x - 1) - 1], by replacing x with x/(x - 1) in f(x)
= x/[x - (x - 1)], by multiplying the numerator and denominator by x - 1
= x/1
= x.
I hope this helps!
2011-03-06 9:31 pm
instead of having f(x), have f(f). So therefore every x in the original equation should be replaced with f, and as f(x)=x/x-1
So the equation would look something like this
ff(x) = (x/x-1)/(x/x-1)-1
if that makes any sense at all?
So the equation would look something like this
ff(x) = (x/x-1)/(x/x-1)-1
if that makes any sense at all?
2011-03-06 9:28 pm
Do you mean:
f(x) = x / (x - 1)
f(f(x))
= f(x) / (f(x) - 1)
= (x / (x - 1)) / ((x / (x - 1)) - 1)
= (x / (x - 1)) / ((x / (x - 1)) - ((x - 1) / (x - 1))
= (x / (x - 1)) / ((x - (x - 1)) / (x - 1))
= (x / (x - 1)) / ((x - x + 1) / (x - 1))
= (x / (x - 1)) / (1 / (x - 1))
= x
f(x) = x / (x - 1)
f(f(x))
= f(x) / (f(x) - 1)
= (x / (x - 1)) / ((x / (x - 1)) - 1)
= (x / (x - 1)) / ((x / (x - 1)) - ((x - 1) / (x - 1))
= (x / (x - 1)) / ((x - (x - 1)) / (x - 1))
= (x / (x - 1)) / ((x - x + 1) / (x - 1))
= (x / (x - 1)) / (1 / (x - 1))
= x
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