Let and for . If the equation has exactly two distinct real solutions, then cannot…

MATHEMATICS · Single correct · AoPS · Mathematics · Special Functions · Special Functions

Problem

Let

f(x)=\begin{cases}|x|,&-3\leq x\leq7,\\2x-7,&7<x\leq10,\end{cases}

and

g(x)=2x+1

for

-3\leq x\leq10

. If the equation

f(|x|)+g(|x|)=k

has exactly two distinct real solutions, then

k

cannot be (a)

32

(b)

33

(c)

34

(d)

35