Let f(x) = x
2
and g(x) = 2x + 1 be two real functions.Find
(f + g) (x), (f –g) (x), (fg) (x), ( ) f
x
g
.
Define the real valued function f : R – {0} → R defined by
1
f x( ) =
x
,
x ∈ R –{0}. Complete the Table given below using this definition. What is the domain
and range of this function?
x –2 –1.5 –1 –0.5 0.25 0.5 1 1.5 2
y =
1
x
… … … … … … … … …
Define the function f: R → R by y = f(x) = x2
, x ∈ R. Complete the
Table given below by using this definition. What is the domain and range of this function?
Draw the graph of f.
x – 4 –3 –2 –1 0 1 2 3 4
y = f(x) = x2
Let N be the set of natural numbers. Define a real valued function
f : N‡ N by f (x) = 2x + 1. Using this definition, complete the table given below.
x 1 2 3 4 5 6 7
y f (1) = … f (2) = … f (3) = … f (4) = … f (5) = … f (6) = … f (7) = …
Examine each of the following relations given below and state in each
case, giving reasons whether it is a function or not?
(i) R = {(2,1),(3,1), (4,2)}, (ii) R = {(2,2),(2,4),(3,3), (4,4)}
(iii) R = {(1,2),(2,3),(3,4), (4,5), (5,6), (6,7)}
Let N be the set of natural numbers and the relation R be defined on
N such that R = {(x, y) : y = 2x, x, y ∈ N}.
What is the domain, codomain and range of R? Is this relation a function?
Let R be the relation on Z defined by R = {(a,b): a, b ∈ Z, a – b is an integer}.
Find the domain and range of R.
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