turkey-yks 2012 Q16

turkey-yks · Other · lys1-math Composite & Inverse Functions Symmetry, Periodicity, and Parity from Composition Conditions

A function f defined on the set of real numbers satisfies the inequality
$$f ( x ) < f ( x + 2 )$$
for every real number x.
Accordingly,
I. $f ( 1 ) < f ( 5 )$ II. $| f ( - 1 ) | < | f ( 1 ) |$ III. $f ( 0 ) + f ( 2 ) < 2 \cdot f ( 4 )$
Which of these statements are always true?
A) Only I
B) Only II
C) I and III
D) II and III
E) I, II and III

A function f defined on the set of real numbers satisfies the inequality

$$f ( x ) < f ( x + 2 )$$

for every real number x.

Accordingly,

I. $f ( 1 ) < f ( 5 )$\\
II. $| f ( - 1 ) | < | f ( 1 ) |$\\
III. $f ( 0 ) + f ( 2 ) < 2 \cdot f ( 4 )$

Which of these statements are always true?

A) Only I\\
B) Only II\\
C) I and III\\
D) II and III\\
E) I, II and III

Paper Questions

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