(1) Determine whether the graph given below represent functions. Give reason for your answers concerning each graph.
(i) |
(ii) |
(iii) |
(iv) |
(2) Let f : A -> B be a function defined by f (x) = (x/2) - 1 where A = {2, 4, 6, 10, 12}, B = {0, 1, 2, 4, 5, 9} .
Represent f by
(i) set of ordered pairs; (ii) a table; (iii) an arrow diagram; (iv) a graph
(3) Represent the function f = {(1, 2),(2, 2),(3, 2),(4, 3),(5, 4)} through (i) an arrow diagram (ii) a table form (iii) a graph Solution
(4) Show that the function f : N -> N defined by f (x) = 2x – 1 is one-one but not onto Solution
(5) Show that the function f : N -> N defined by f (m) = m^{2} + m + 3 is one-one function. Solution
(6) Let A = {1, 2, 3, 4} and B = N . Let f : A -> B be defined by f (x) = x^{3} then, (i) find the range of f (ii) identify the type of function Solution
(7) In each of the following cases state whether the function is bijective or not. Justify your answer.
(i) f : R -> R defined by f (x) = 2x +1
(ii) f : R -> R defined by f (x) = 3 – 4x^{2 }
(8) Let A = {−1, 1}and B = {0, 2} . If the function f : A -> B defined by f(x) = ax + b is an onto function? Find a and b.
(9) If the function f is defined by
find the values of
(i) f (3) (ii) f (0) (iii) f (−1.5) (iv) f (2)+ f (−2) Solution
(10) A function f : [−5,9] -> R is defined as follows:
Find (i) f (−3) + f (2) (ii) f (7) - f (1) (iii) 2f (4) + f (8)
(iv) [2f(-2) - f(6)] / [f(4) + f(-2)] Solution
(11) The distance S an object travels under the influence of gravity in time t seconds is given by
S(t) = (1/2) gt^{2} + at + b
where, (g is the acceleration due to gravity), a, b are [constants. Check if the function S(t) is one-one.
(12) The function ‘t’ which maps temperature in Celsius (C) into temperature in Fahrenheit (F) is defined by
t(C) = F where F = (9/5) C + 32 .
Find, (i) t(0) (ii) t(28) (iii) t(-10)
(iv) the value of C when t (C) = 212
(v) the temperature when the Celsius value is equal to the Farenheit value. Solution
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