Question

Find the domain and range
of following functions
1)z=1/xy
2) z=y-x
3) z=√y-x(whole under root)​

Answer 1

Answer:

1)

z = 1 / xy

Because it the rational function with singular point at x = y = 0 So

Domain = { (x , y) ∈ R² : x = y ≠ 0 }

Range = Real number.

2)

z = y - x

Because it is the polynomial function with no singular points so

Domain = { (x , y) ∈ R²}

Range = Real number.

3)

z = √(y - x)

Because it the function with radical and we known that radical of negative number is complex number that is not real so we have to set y ≥ x to get positive answer So

Domain = { (x , y) ∈ R² : x ≤ y }

Range = Real number.