Domain of a Square Root Function

The domain of a square root function given by y = k √x is determined by the following:

1. Range is a real number. The range is ≥ 0 when k ≥ 0, and the range is < 0 when k < 0.
2. The domain is x ≥ 0.

Example:

Find the domain and range of the following function

1. y =
   Solution :
   As stated above, the linear function in a square root should always have its value greater than or equal to zero.
   Therefore, the domain of y will be given by x – 1 ≥ 0 or x ≥ 1.
   For the range of y, the value of the square root function will always be greater than or equal to zero.
   Hence the range of y is ≥ 0.
2. y =
   Solution:
   Domain: x ≥ 0
   For the range: since
   ≥ 0, y ≥ 0 + 5 or y ≥ 5.
3. y =
   Solution :
   To find the domain, we use the condition that 20-9x ≥0.
   Add 9x on both sides: 20 ≥ 9x.
   Divide both sides with 9: 20/9 ≥ x.
   Hence the domain of y is x ≤ 20/9.
   The range will be the same as for
   y =
   because the square root function will always give a value ≥ 0.

Try this problem

1. Find the domain of
   1. x > 9/5
   2. x < 9/5
   3. x ≥ 9/5
   4. x ≤ 9/5

Answer: C

Explanation :

The given square root function is

The square root function is defined for f(x)≥0.

Hence, f(x)= 5x-9>=0.

Add 9 to both the sides: 5x ≥9.

Divide by 9:

x ≥ 9/5