Hi,
For which of the following is f(x) = f(1-x) for all x ?
Choices are:
1. f(x) = 1-x
2. f(x) = 1-x^2
3. f(x) = x^2 - (1-x)^2
4. f(x) = x^2(1-x)^2
5. f(x) = x / 1-x
The answer is choice 4 but could someone please explain the solution ?
Thanks,
Krish
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Sachindh
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A simple way is to replace the 'x with (1-x) and the value of f(x) should not change.KrishMBA wrote:Hi,
For which of the following is f(x) = f(1-x) for all x ?
Choices are:
1. f(x) = 1-x
2. f(x) = 1-x^2
3. f(x) = x^2 - (1-x)^2
4. f(x) = x^2(1-x)^2
5. f(x) = x / 1-x
The answer is choice 4 but could someone please explain the solution ?
Thanks,
Krish
So, If you look at the options only 4 is that which does not change if I change x by (1-x).
I hope it helps.
Thanks
-
Sachindh
- Senior | Next Rank: 100 Posts
- Posts: 37
- Joined: Wed Sep 17, 2008 8:17 pm
- Location: India
- Thanked: 4 times
Take option 4KrishMBA wrote:Hi Sachin,
Thanks for your reply... But could you please provide an example or show how option 4 is correct ...
f(x) = x^2(1-x)^2
f(1-x) = (1-x)^2(1-(1-x))^2
f(1-x) = (1-x)^2 (1-1+x)^2
f(1-x) = (1-x)^2 (0+x)^2
f(1-x) = f(x)
Now in other cases this shall not be true.
Thanks
