tmua.me Tau Paper 2 · Question 13

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tmua.me Tau Paper 2 · Q13

Paper 2Functions & graphsLogic & proof

Let $T$ be the set of all possible values of $f(2)-\lambda$ , where $\lambda$ is a non-zero real number and $f:\mathbb R\to\mathbb R$ satisfies

f\bigl(x^2+f(y)\bigr)=\lambda y+(\lambda-2)f(x)^2 \qquad\text{for every real }x,y.

No continuity or differentiability is assumed.

What is the sum of the squares of the distinct elements of $T$ ?

12

16

4

8

10

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