Question

For all real numbers x, the function f(x) satisfies 2f(x)+f(1-x)=x^2. Find f(5)??

Answer 1

34/3

Answer 2

how have you found that???

Answer 3

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

Answer 4

substitute x -> 1-x

Answer 5

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

Answer 6

2[x^2 - 2f(x)] + f(x) = (1-x)^2, ie:
2x^2 - 3f(x) = (1-x)^2, ie:
3f(x) = 2x^2 - (1-x)^2 = x^2 + 2x - 1

Answer 7

f(x) = (x^2 + 2x - 1) / 3

Answer 8

f(5)= ?? (u knw it well) by substituting 5

Answer 9

you get 34/3

Answer 10

oh ok i understand it now... thanx a lot))

Answer 11

come on maths chat