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MATH / Let R be the set of real numbers. Let f:R→R be a function such that for all real numbers x and y, f(x²)+f(y²)=f(x+y)²−2xy.Let S=∑_(n=−2019)²⁰¹⁹f(n).Determine the number of possible…

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problem

Let R\mathbb{R} be the set of real numbers. Let f:R→Rf : \mathbb{R} \to \mathbb{R} be a function such that for all real numbers xx and y,y, f(x2)+f(y2)=f(x+y)2−2xy.f(x^2) + f(y^2) = f(x + y)^2 - 2xy.Let S=∑n=−20192019f(n).S = \sum_{n = -2019}^{2019} f(n).Determine the number of possible values of S.S.
Plain-text mathematical notation (without MathML)
Let R be the set of real numbers.  Let f:R→R be a function such that for all real numbers x and y,
f(x²)+f(y²)=f(x+y)²−2xy.Let
S=∑_(n=−2019)²⁰¹⁹f(n).Determine the number of possible values of S.
Original LaTeX notation
Let $\mathbb{R}$ be the set of real numbers.  Let $f : \mathbb{R} \to \mathbb{R}$ be a function such that for all real numbers $x$ and $y,$
\[f(x^2) + f(y^2) = f(x + y)^2 - 2xy.\]Let
\[S = \sum_{n = -2019}^{2019} f(n).\]Determine the number of possible values of $S.$

level

Level 5

type

Intermediate Algebra

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Source and history

task_id
e3828ede-d1fa-5afd-92d3-7b6275a10ee9
task_key
intermediate~5falgebra--test--e3828ede-d1fa-5afd-92d3-7b6275a10ee9
task_revision_id
1
config / split
intermediate_algebra / test

Official source

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