PRACTICE PROBLEMS ON FINDING DOMAIN AND RANGE OF A FUNCTION

Find the domain and range of following modulus function

1)  f(x)  =  |x - 3|

2)  f(x)  =  1 - |x - 2|

3)  f(x)  =  |x - 4|/(x - 4)

Solution

Answers :

1)   Domain : R, Range : [0, ∞)

2)  Domain : All the real values R, Range : (- ∞, 1]

3)  Domain :  R - {4}, Range : [-1, 1]

Find the domain of the following rational functions

1)  f(x)  =  (x - 1)/(x - 3)

2)  f(x)  =  (2x - 3)/(x2 - 3x + 2)

3)   √(x - 2)

4)  f(x)  =  √(4 - x) + (1/√(x2 - 1))

5)  f(x)  =  (2x + 1)/(x2 - 9)

Solution

6)  f(x)  =  x/(1 + x2)

7)  f(x)  =  3/(2 - x2)

Solution

Answers :

1)  Domain :  R - {3}

2)  Domain : R - {1, 2}

3)  Domain : [2, ∞)

4)  Domain : (-∞, -1) U (1, 4]

5)  Domain : R - [-3, 3]

6)  Domain : All the real values R, Range : [-1/2, 1/2]

7)  Domain : R - {± √2}, Range : (-∞, 0) U [3/2, ∞)

Find the domain of the following radical function

1)  y = √(x-2)

2)  y  =  √(3–2x)

3)  y  =  1/(x+2)

4)   y  =  1/√(5+2x)

5)  y  =  √[x(x – 2)]

6) y  = (1/√x) + (1/√(2 – x))

7)  y  =  √(x2 – 3x)

8)  y  =  y  =  √(x2 – 3x)

Solution

Answers :

1)  Domain : [2, ∞)

2)  Domain : (-∞, 3/2]

3)  Domain : (-2, ∞)

4)  Domain : (-5/2, ∞)

5)  Domain : (-∞, 0] u [2, ∞)

6)  Domain : (0, 2)

7)  Domain : (-∞, 0] u [3, ∞)

8)  Domain :  (-∞, -3] u (1, ∞)

Find the domain of the following square root function

1)  f(x)  =  √(x - 2)

2)  f(x)  = 1/ √(1 - x)

3)  f(x)  = √(4 - x2)

4)  f(x)  = √(4 - x) + 1/√(x2 - 1)

Solution

Answers :

1)  Domain : [2, ∞)

2)  Domain : (∞, 1)

3)  Domain : [-2, 2]

4)  Domain : (-∞, -1) U (1, 4]

Find the domain and range of the following trigonometric function

1)  f(x)  =  1/(2 - sin 3x)

2)  f(x)  =  1/(1 - 2 cos x) 

Solution

Answers :

1) Domain :  All the real values, Range :  [1/3, 1]

2)  Range : [-1, 1/3]

Find the domain and range of the following quadratic function

1)  y  =  x2 + 5x + 6

2)  y  =  -2x2 + 5x - 7

Solution

Answers :

1)  Domain : {x │ x Є R}, Range : {y │ y ≥ -0.25}

2)   Domain : {x │ x Є R}, Range : {y │ y ≤ -3.875}

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