Question

Find the sketch the domain of the function \(f\left( {x,y} \right) = \sqrt {2x - y} \)

Short answer

The domain of the function f is \(\left\{ {\left( {x,y} \right)/2x - y \ge 0} \right\}\)

Step-by-step solution

Step 1:- Consideration

Let \(f\left( {x,y} \right) = \sqrt {2x - y} \) is a function

Step 2:- Substitution

Let \(\sqrt {2x - y} \) be the function and the function to be exist it must be greater than (or) equal to zero be \((2x - y) \ge 0{\rm{ }}or{\rm{ }}(2x) \ge y\)

Therefore domain of f is \(\left\{ {\left( {x,y} \right)/(2x - y) \ge 0} \right\}{\rm{ or }}\left\{ {\left( {x,y} \right)/(2x) \ge y} \right\}\)

Hence, the domain of f is \(\left\{ {\left( {x,y} \right)/(2x - y) \ge 0} \right\}\)

Graph