## About "Domain of a square root function worksheet"

Domain of a square root function worksheet :

Here we are going to see some practice questions on domain of square root functions.

## Domain of a square root function worksheet - Practice questions

(1)  Find the domain of the following function

f(x)  =  √(x - 2)

(2)  Find the domain of the following function

f(x)  = 1/ √(1 - x)

(3)  Find the domain of the following function

f(x)  √(4 - x2)

(4)  Find the domain of the following function

f(x)  √(4 - x) + 1/√(x2 - 1)

## Domain of a square root function worksheet - Solution

Question 1 :

Find the domain of the following function

f(x)  =  √(x - 2)

Solution :

Step 1 :

Since the square root sign is in numerator, we need to equate the expression inside the radical sign to ≥ 0

x - 2 ≥ 0

Step 2 :

x - 2 + 2 ≥ 0 + 2

x  ≥ 2

Step 3 :

Possible values of x are between [2, ∞)

Step 4 :

Hence the domain of the given function is x ∈ [2, ∞)

Question 2 :

Find the domain of the following function

f(x)  = 1/ √(1 - x)

Solution :

Step 1 :

Since the square root sign is in numerator, we need to equate the expression inside the radical sign to > 0

1 - x ≥ 0

Step 2 :

Subtract 1 on both sides

1 - x - 1  > 0 - 1

-x  > -1

Divide by -1 on both sides

-x/(-1)  >  -1/(-1)

x  <  1

Step 3 :

Possible values of x are between (∞, 1)

Step 4 :

Hence the domain of the given function is x ∈ (∞, 1)

Question 3 :

Find the domain of the following function

f(x)  √(4 - x2)

Solution :

Step 1 :

Since the square root sign is in numerator, we need to equate the expression inside the radical sign to ≥ 0

4 - x2 ≥ 0

Step 2 :

4 - x2 ≥ 0

Subtract 4 on both sides

4 - x2 - 4 ≥ 0 - 4

- x≥ -4

x≤ 4 ==> x = ± 2

Step 3 :

Possible values of x are between [-2, 2]

Step 4 :

Hence the domain of the given function is x ∈ [-2, 2]

Question 4 :

Find the domain of the following function

f(x)  √(4 - x) + 1/√(x2 - 1)

Solution :

Step 1 :

The given function has two parts.

Part 1 is √(4 - x)

Part 2 is 1/√(x2 - 1)

Since part 1 is having square root sign in the numerator,  we need to equate the expression inside the radical sign to ≥  0.

4 - x  0

Since part 2 is having square root sign in the denominator ,  we need to equate the expression inside the radical sign to > 0

x2 - 1 > 0

Step 2 :

 4 - x ≥ 0Subtract 4 on both sides4 - x - 4 ≥ 0 - 4-x ≥ -4x ≤ 4 x2 - 1 > 0Add 1 on both sidesx2 - 1 + 1 > 0 + 1x2 >  1x >  ±1

Step 3 :

Possible values of x are between (-∞, -1) U (1, 4]

Step 4 :

Hence the domain of the given function is x ∈ (-∞, -1) U (1, 4]

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