Exercise 1.4: Types of Functions

Exercise 1.4

1. Determine whether the graph given below represent functions. Give reason for your answers concerning each graph.

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

4. Show that the function f : N → N defined by f (x) = 2x – 1 is one-one but not onto.

5. Show that the function f : N → N defined by f (m) = m2 + m + 3 is one-one function.

6. Let A = {1, 2, 3, 4} and B = N Let f: A → B be defined by f (x) = x3 then,

(i) find the range of f 

(ii) identify the type of function 

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 – 4x2

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 f (x)= find the values of

(i) f (3)

(ii) f (0)

(iii) f (−1 ⋅ 5)

(iv) f (2) + f (−2)

10. A function f : [−5, 9] → R is defined as follows:

f (x) = 

Find 

(i) f (−3) + f (2)

(ii) f (7) - f (1)

(iii) 2f (4) + f (8)

(iv) 

11. The distance S an object travels under the influence of gravity in time t seconds is given by S(t) = 1/2 gt2 + 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.

Answers:

1. (i) Not a function (ii) function (iii) Not a function (iv) function

2.(i) {(2,0),(4,1),(6,2),(10,4),(12,5)}

6.(i) {1, 8, 27, 64} (ii) one-one and into function

7.(i) Bijective function (ii) Not bijective function 8. 1,1

9.(i) 5 (ii) 2 (iii) -2. 5 (iv) 1

10.(i) 2 (ii) 10 (iii) 178 (iv) -9/17

11. Yes 12.(i) 32°F (ii) 82. 4°F (iv) 24°C

(iv) 100°C (v) − 40°