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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}

 

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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.

 

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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.

 

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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}

 

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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}

 

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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}

 

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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}

 

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Question 8: Find the range of the function f(x) from the graph?


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.

 

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Question 9: Find the domain of the function f(x) from the graph?


Graph 1

 

(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.

 

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Question 10: Find the domain and range of the function from the graph?


Graph 2

 

 

Question 10 options


Answer: (a)

Explanation: Get it resolve from the Graph.

 

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