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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PRACTICE PROBLEMS ON FINDING DOMAIN AND RANGE OF A FUNCTION

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