goyalsau wrote:Rahul@gurome wrote:You can easily see that it is option d.
f(1-x) = (1-x)^2 * {1-(1-x)}^2 = (1-x)^2 *x^2 = x^2 *(1-x)^2 = f(x).
Rahul can you plz. explain this one. a bit further i am not able to understand it,
What the question is asking: which of the functions would have the same value if 'x' were replaced with '1-x'
Let us now consider replacing x with 1-x in each of the answer choices.
a. f(x)=1-x
Substitute x with 1-x in the function. We have f(x) = 1 - (1-x) = 1 - 1 + x = x
Clearly, f(x) = 1-x and f(1-x) = x are not the same. Eliminate this answer.
b. f(x)=1-x(squared)
Substitute x with 1-x in the function. We have f(x) = 1 - [(1-x)^2] = 1 - (1 + x^2 - 2x) = 2x - x^2
Clearly, f(x) = 1-x^2 and f(1-x) = 2x - x^2 are not the same. Eliminate this answer.
c. f(x)=x(squared) - (1-x)squared
Substitute x with 1-x in the function. We have f(x) = (1-x)^2 - [1 - (1-x)]^2 = (1 + x^2 - 2x) - x^2 = x^2 - 2x
Clearly, f(x) = x^2 - (1-x)^2 and f(1-x) = x^2 - 2x are not the same. Eliminate this answer.
d. f(x)=x(squared) (1-x) squared
Substitute x with 1-x in the function. We have f(x) = (1-x)^2 * [1 - (1-x)]^2 = (1 + x^2 - 2x) * x^2 = (1-x)^2 * x^2
If you note, (1-x)^2 * x^2 = f(x)
Clearly, f(x) = x^2 - (1-x)^2 and f(1-x) = x^2 - (1-x)^2 are the same. This is the right answer. At this point, you can mark this answer and proceed to the next question. However, for the sake of completeness, let us work out the last answer choice too.
e. f(x) = x/1-x
Substitute x with 1-x in the function. We have f(x) = (1-x) / [1 - (1-x)] = (1-x)/x
Clearly, f(x) = x/1-x and f(1-x) = (1-x)/x are not the same. In fact, one is the reciprocal of the other. Eliminate this answer.
For help, try using this site:
https://www.brightstorm.com/math/algebra ... -functions
HTH
