Here the step involves substituting 1-x for x in function equation.

Suppose f(x)=1-x

Now sub 1-x for x then f(1-x)=1-(1-x)=x

f(x)!=f(1-x)

Only D satisfy the condition.

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

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

f(x)=f(1-x)

Pick D

selango wrote:Here the step involves substituting 1-x for x in function equation.

Suppose f(x)=1-x

Now sub 1-x for x then f(1-x)=1-(1-x)=x

f(x)!=f(1-x)

Only D satisfy the condition.

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

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

f(x)=f(1-x)

Pick D

Can you please explain this step,
and is there any other way to solve these type of questions?

Gurpinder wrote:

Since the correct answer has to work for all values of x, we can plug in our own value for x.

Plug in x=2. Then f(x) = f(2) and f(1-x) = f(1-2) = f(-1). The question becomes:

For which of the following functions does f(2) = f(-1)?

Answer choice A:
f(2) = 1-2 = -1.
f(-1) = 1-(-1) = 2.
Doesn't work.

Answer choice B:
f(2) = 1 - 2^2 = -3.
f(-1) = 1 - (-1)^2 = 0.
Doesn't work.

Answer choice C:
f(2) = 2^2 - (1-2)^2 = 4 - 1 = 3.
f(-1) = (-1)^2 - [1-(-1)]^2 = 1-4 = -3.
Doesn't work.

Answer choice D:
f(2) = 2^2 * (1-2)^2 = 4 * 1 = 4.
f(-1) = (-1)^2 * [1-(-1)]^2 = 1 * 4 = 4.
Success!

Answer choice E:
f(2) = 2/(1-2) = -2.
f(-1) = (-1)/[(1-(-1)] = -1/2.
Doesn't work.

The correct answer is D.

thanks Gmatguruny for such a nice explanation.
I was thinking what can be a easy way,
you just made it look so simple.

hey Mitch,

using your method, a question such as this one would be


lets say a=1 and b=2

so f(3) = f(1) + f(2)


So the question becomes for which of the following functions does f(1) + f(2) equal f(3)?

Is that right?

Gurpinder wrote:hey Mitch,

using your method, a question such as this one would be


lets say a=1 and b=2

so f(3) = f(1) + f(2)


So the question becomes for which of the following functions does f(1) + f(2) equal f(3)?

Is that right?

Exactly right!

Thank you!

For the first time in my life, I understand functions! =)