For every pair of continuous functions such that

MATHEMATICS · Single correct · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

For every pair of continuous functions

f, g: [0, 1] \to R

such that

\max \{f(x): x \in [0, 1]\} = \max \{g(x): x \in [0, 1]\}

, which statement(s) is (are) correct? (1)

[f(c)]^2 + 3f(c) = [g(c)]^2 + 3g(c)

for some

c \in [0, 1]

(2)

[f(c)]^2 + f(c) = [g(c)]^2 + 3g(c)

for some

c \in [0, 1]

(3)

[f(c)]^2 + 3f(c) = [g(c)]^2 + g(c)

for some

c \in [0, 1]

(4)

[f(c)]^2 = [g(c)]^2

for some

c \in [0, 1]