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2015 Algebra #8

Source:

July 1, 2022

2015Algebra Test

Problem Statement

Let

\{x\}

denote the fractional part of

x

, which means the unique real

0\leq\{x\}<1

such that

x-\{x\}

is an integer. Let

f_{a,b}(x)=\{x+a\}+2\{x+b\}

and let its range be

[m_{a,b},M_{a,b})

. Find the minimum value of

M_{a,b}

as

a

and

b

range along all real numbers.

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