Another question from MGMAT guide

[sch]

For which of the following functions does F(x)=F(2-x)

Answer is f(x)=2x-x^2 They solved it by plugging in 4. But that yeilds -8 for F(x) and -6 for F(2-x).

I cant figure out how that can be an answer when the values are different in each functions, and they are clearly not equal to eachother. I am a little slow in math and even simple problems like these are a challange for me, if anyone can explain me how this is an answer I would greatly apriciate it.

[sk818020]

They were right

F(x)=F(4)=

2(4)-4^2= 8-16 = -8

F(2-x)=F(2-4)=F(-2)=

2(-2)-(-2)^2 = -4-4 = -8

[harshavardhanc]

For which of the following functions does F(x)=F(2-x)

Answer is f(x)=2x-x^2 They solved it by plugging in 4. But that yeilds -8 for F(x) and -6 for F(2-x).

I cant figure out how that can be an answer when the values are different in each functions, and they are clearly not equal to eachother. I am a little slow in math and even simple problems like these are a challange for me, if anyone can explain me how this is an answer I would greatly apriciate it.

another way to go about it :

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

or x [ 2 - x ] (taking x common )

now, if you put (2-x) in place of x or if you try to find out f (2-x), you'll get :

(2-x) [ 2 - (2-x) ]

= (2-x) [ 2- 2 + x ]

= x (2-x)

which is equal to f (x). You've got your answer.

HTH.