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## Domain of a Square Root Function

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

• Range is a real number. The range is ≥ 0 when k ≥ 0, and the range is < 0 when k < 0.

• 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

a.
x > 9/5

b.
x < 9/5

c.
x ≥ 9/5

d.
x ≤ 9/5

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