**Relations and Functions Worksheet :**

Here we are going to see some practice questions on relations and functions.

(1) Let f = {(x, y) | x, y ∈ N and y = 2x} be a relation on ℕ. Find the domain, co-domain and range. Is this relation a function? Solution

(2) Let X = {3, 4, 6, 8}. Determine whether the relation ℝ = {(x, f (x)) | x ∈ X, f (x) = x^{2} + 1} is a function from X to ℕ ? Solution

(3) Given the function f : x -> x^{2} −5x + 6 , evaluate

(i) f (-1)

(ii) f (2a)

(iii) f (2)

(iv) f (x −1) Solution

(4) A graph representing the function f (x) is given figure

it is clear that f (9) = 2.

(i) Find the following values of the function

(a) f (0) (b) f (7) (c) f (2) (d) f (10)

(ii) For what value of x is f (x) = 1?

(iii) Describe the following (i) Domain (ii) Range.

(iv) What is the image of 6 under f ? Solution

Let f (x) = 2x + 5. If x ≠ 0 then find [f(x + 2) - f(2)] / x

(5) A function f is defined by f (x) = 2x – 3

(i) find [f(0) + f(1)]/2

(ii) find x such that f (x) = 0.

(iii) find x such that f (x) = x .

(iv) find x such that f (x) = f (1−x) . Solution

(6) An open box is to be made from a square piece of material, 24 cm on a side, by cutting equal squares from the corners and turning up the sides as shown. Express the volume V of the box as a function of x.

(7) A function f is defined by f (x) = 3−2x . Find x such that f (x^{2}) = (f (x))^{2} Solution

(8) A plane is flying at a speed of 500 km per hour. Express the distance d travelled by the plane as function of time t in hours. Solution

(9) The data in the adjacent table depicts the length of a woman’s forehand and her corresponding height. Based on this data, a student finds a relationship between the height (y) and the forehand length(x) as y = ax +b , where a, b are constants.

(i) Check if this relation is a function.

(ii) Find a and b.

(iii) Find the height of a woman whose forehand length is 40 cm.

(iv) Find the length of forehand of a woman if her height is 53.3 inches. Solution

After having gone through the stuff given above, we hope that the students would have understood, "Relations and Functions Worksheet".

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