(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
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