tmua.me Medium Set A Paper 1 · Question 7

tmua.me papers

tmua.me Medium Set A Paper 1 · Q7

Paper 1Functions & graphsAlgebra

A function $f$ , defined for all real numbers, satisfies

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

for every real $x$ . For which values of the real constant $k$ does the equation

f(|x|)=k

have exactly four distinct real solutions?

k>-\dfrac23

k\geq\dfrac23

-\dfrac23\leq k<\dfrac23

-\dfrac23<k\leq\dfrac23

0<k<\dfrac23

-\dfrac23<k<\dfrac23

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