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)
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)
6) f(x) = x/(1 + x2)
7) f(x) = 3/(2 - x2)
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) |
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)
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)
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
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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