tmua.me Extreme Set C Paper 2 · Question 7

A real-valued function $f$ , defined for every real number, satisfies

f(x)+f(-x)=2x^2+2,\qquad f(x)f(-x)=x^4+x^2+1

for every real $x$ .

Consider the following statements.

$f$ must be a quadratic polynomial.
The least value of $f$ is $3/4$ .
For every real $y>3/4$ , the equation $f(x)=y$ has exactly two distinct real solutions.

Which of these statements must be true?

AI only

BII and III only

CI and II only

DI and III only

EII only

FI, II and III

examday