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jmc

algebra junior

Problem

Let

f(a,b) = \left\{ \renewcommand{\arraystretch}{3} \begin{array}{cl} \dfrac{ab - a + 2}{2a} & \text{if $a + b \le 3$}, \\ \dfrac{ab - b - 2}{-2b} & \text{if $a + b > 3$}. \end{array} \renewcommand{\arraystretch}{1} \right.

Find

f (2, 1) + f (2, 4) .

Solution

We have that

f (2, 1) = \frac{2 \cdot 1 - 2 + 2}{4} = \frac{1}{2},

and

f (2, 4) = \frac{2 \cdot 4 - 4 - 2}{- 8} = - \frac{1}{4},

so

f (2, 1) + f (4, 2) = \frac{1}{4} .

Final answer

\frac{1}{4}