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diegoasaavedra
- Newbie | Next Rank: 10 Posts
- Posts: 8
- Joined: Mon Sep 18, 2006 10:40 pm
Check one by one the choices...diegoasaavedra wrote:For which of the following functions is f(x)= f(1-x) for all x
a- f(x)= 1-x
b- f(x)= 1-x^2
c- f(x)= x^2-(1-x)^2
d- F(x)= x^2(1-x)^2
e- f(x)= x/1-x
Answer is D, can some body help with this?
Thanks
A. If f(x) = 1 - x, then f (1 - x) = 1 - (1 - x) = x; not the same.
B. If f(x) = 1 - x^2, then f (1 - x) = 1 - (1 - x) ^2 = 2 x - x^2; not the same.
C. If f(x) = x^2 - (1 - x) ^2 = 2 x - 1, then f (1 - x) = (1 - x) ^2 - x^2 = 1 - 2 x; not the same.
D. If f(x) = x^2 (1 - x) ^2, then f (1 - x) = (1 - x) ^2 (1 - 1 + x) ^2 = x^2 (1 - x) ^2; the same.
E. Ignore E.
[spoiler]Take D[/spoiler]
