Problem Solving

For which of the following functions f is f(x)=f(1-x) for all x ?

f(x)=1-x
f(x)=1-x^2
f(x)=x^2(1-x)^2
f(x)=x^2(1-x)^2

The answer is D

moneyman wrote:For which of the following functions f is f(x)=f(1-x) for all x ?

f(x)=1-x
f(x)=1-x^2
f(x)=x^2(1-x)^2
f(x)=x^2(1-x)^2

The answer is D

Look Moneyman, ur option C and D are referring the same value. Now,
f(x) = x^2(1 - x)^2
Now put 1-x in place of x -
f(1 - x) = (1 - x)^2(1 - (1 - x))^2
= (1 - x)^2x^2 = f(x)

So go for option C or D.

Hello,

NIce handle Camitava! I don't see your reasoning for plugging in 1-x for all of X. I am used to practicing on numbers that are plugged in. CAn you help?

Enginpasa1 wrote:Hello,

NIce handle Camitava! I don't see your reasoning for plugging in 1-x for all of X. I am used to practicing on numbers that are plugged in. CAn you help?

Enginpasa1, I will suggest that depending upon the Qs pattern, u have to chose between the approaches - 1. To pick up numbers or 2. To deal with x and some unknown variables like - y, z and so on.
Now I believe this Qs is better solved by putting x - unknown variables - rather than putting some numbers against x.
However, if you want, take x = 2, 3, 4, 5, 6 and so on. Even if u take these numbers, u will find that C or D is the best option to chose.

Hey there,

This problem was discussed earlier. See the link, please.

https://www.beatthegmat.com/gmat-prep-fu ... html#25298