Functions $

Algebra Level 3

Let us define a binary operator, $ \$ such that

$ ( a , b ) = { a b − a + 2 2 a , if a + b ≤ 3 a b − b − 2 − 2 b , if a + b > 3 \$(a,b) = \begin{cases} \frac{ab-a+2}{2a} & , \quad & \text{ if } a+b \leq 3 \\ \frac{ab-b-2}{-2b} & , \quad & \text{ if } a+b > 3 \\ \end{cases}

Find $ ( 2 , 1 ) + $ ( 2 , 4 ) \$(2,1) + \$(2,4) .

2 10 1 4 \frac14 1 2 \frac12 6

Ameer Deeb by Ameer Deeb , 25, Israel

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1 solution

Ameer Deeb
Feb 23, 2016

start step by step: $(2,1)=2+1<=3 so 6-1+2\4= 1\2 $(2,4)2+4>3 so 8-4-2-8= -1\4 1\2+(-1\4)=1\4

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