Evaluate each option
1. f(x)=1-x
Now, check what would be f(1-x). Replace x in the above eq with 1-x
f(1-x) = 1-(1-x) = x
So we see that f(1-x) neq f(x)
2. f(x) = x^2-(1-x)^2
f(1-x) = (1-x)^2 - (1-(1-x))^2 = (1-x)^2 - x^2
Again f(x) neq f(1-x)
Similarly, do the same for C, D and E
You will see that for D
f(x)=(f(1-x)=x^2*(1-x)^2
Hope this clears your doubt
1. f(x)=1-x
Now, check what would be f(1-x). Replace x in the above eq with 1-x
f(1-x) = 1-(1-x) = x
So we see that f(1-x) neq f(x)
2. f(x) = x^2-(1-x)^2
f(1-x) = (1-x)^2 - (1-(1-x))^2 = (1-x)^2 - x^2
Again f(x) neq f(1-x)
Similarly, do the same for C, D and E
You will see that for D
f(x)=(f(1-x)=x^2*(1-x)^2
Hope this clears your doubt
