Domain and Range:
The domain of a function is the set of all the function's potential inputs.A domain is a collection of "all the values" that make up a function.Example, considered a function f(x) = 3x, then the domain is the all the possible values of x = {1,2,3,..}.
The set of all the outputs of a function is its range.
Pre-images are domain items, whereas images are mapped co-domain(range) components.
In the above example, the range is {3,6,9,12,...}, all the possible output of function f(x).
Domain and Range Sample Questions:
Question 1: Find the domain of f(x),
f(x) = 2x^2 + 4x + 2
(a) (-∞, +∞)
(b) (+2, -2)
(c) (-2, +2)
(d) (-2, -2)
Answer: (a)
Explanation: Here, {x|x∈R}
Question 2: Find the domain of f(x),
f(x)= 1/√x-5
(a) (-∞, +∞)
(b) (-∞, 5)
(c) (5, -∞)
(d) (5, ∞)
Answer: (d)
Explanation: Value of x is always greater than 5, x>5, x not equal to 5.
Question 3: f(x) = x^2 + 2
g(x) = √x-4
Find the domain of (fOg)(x)?
(a) (-4, +∞)
(b) (4, ∞)
(c) (-∞, 4)
(d) (∞, -4)
Answer: (b)
Explanation: We conclude that the value of x starts from 4 and goes to infinity.
Question 4: Find the domain of f(g(x)),
f(x) =√x-4, g(x) = 3/(x - 9)
(a) (9, 21/2)
(b) (9, -21/2)
(c) (-9, 21/2)
(d) (-9, -21/2)
Answer: (a)
Explanation: Value of x: {x | 9 < x ≤ 21/2}
Question 5: Find the domain of f(g(x))
f(x) =3x - 4, g(x) = √x+2
(a) (-2, 2)
(b) (-2, ∞)
(c) (-∞, ∞)
(d) (-∞, 2)
Answer: (b)
Explanation: Value of x: {x | x ≥ -2}
Question 6: Find the range of f(x)
f(x) = 2x^2 + 4x + 2
(a) (0, -∞)
(b) (-∞, 0)
(c) (0, ∞)
(d) (-∞, ∞)
Answer: (c)
Explanation: {y | y ≥ 0}
Question 7: Find the range of f(x)
f(x) = 1/√x-5
(a) (0, ∞)
(b) (-∞, 0)
(c) (0, -∞)
(d) (-∞, ∞)
Answer: (a)
Explanation: {y | y > 0}
Question 8: Find the range of the function f(x) from the graph?
(a) (0, ∞), {y | y > 0}
(b) (-∞, 0), {y | y > 0}
(c) (0, ∞), {y | y ≥ 0}
(d) (-∞, 0), {y | y ≥ 0}
Answer: (a)
Explanation: Get it resolve from the Graph.
Question 9: Find the domain of the function f(x) from the graph?
(a) (-∞, ∞), {x | x ≠ 0}
(b) (-∞, 0)U(0, ∞), {x | x ≠ 0}
(c) (-∞, 0)U(0, ∞), {x | x = 0}
(d) (-∞, ∞), {x | x = 0}
Answer: (b)
Explanation: Get it resolve from the Graph.
Question 10: Find the domain and range of the function from the graph?
Answer: (a)
Explanation: Get it resolve from the Graph.
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