Question

The expression \(\frac{{\left( {x + y} \right) - \left| {x - y} \right|}}{2}\) is equal to
1. the maximum of x and y
2. the minimum of x and y
3. 2
4. none of the above

Answer 1

Correct Answer - Option 2 : the minimum of x and y

Case 1: When x > y

\(\frac{{\left( {x + y} \right) - \left| {x - y} \right|}}{2} = \frac{{\left( {x + y} \right) - \left( {x - y} \right)}}{2} = y\)

Case 2: When x < y

\(\frac{{\left( {x + y} \right) - \left| {x - y} \right|}}{2} = \frac{{\left( {x + y} \right) - \left( {y - x} \right)}}{2} = x\)

The given function can be written as

\(\frac{{\left( {x + y} \right) - \left| {x - y} \right|}}{2} = \left\{ {\begin{array}{*{20}{c}} {y,\;x > y}\\ {x,\;x < y} \end{array}} \right.\)

So, the given expression is equal to the minimum of x and y.