exam Maths Puzzle Numerical Ability

I have the following problem:

If 2f(x)+f(1-x)=x2(this should be "x-squared"), what is f(x)?

The answer is f(x)=1/3x2+2/3x-1/3. But how in the world do you get to this answer

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exam Other Question

Could someone please assist me by solving this logarithmic equation step-by-step for future reference. Thank you.

log(7y + 1) = 2log(y+3)-log2
Please help w/ the following:
Find the rational roots of F. List any irrational roots correct to two decimal places.
f(x)= x^4+7x^3+x^2-35x-30
Thank you.