20 Let f = {(1,1), (2,3), (0, –1), (–1, –3)} be a linear function from Z into Z.
Find f(x).
Let R be a relation from Q to Q defined by R = {(a,b): a,b ∈ Q and
a – b ∈ Z}. Show that
(i) (a,a) ∈ R for all a ∈ Q
(ii) (a,b) ∈ R implies that (b, a) ∈ R
(iii) (a,b) ∈ R and (b,c) ∈ R implies that (a,c) ∈R
18 Let R be the set of real numbers.
Define the real function
f: R→R by f(x) = x + 10
and sketch the graph of this function.
Find the range of each of the following functions.
(i) f (x) = 2 – 3x, x ∈ R, x > 0.
(ii) f (x) = x
2
+ 2, x is a real number.
(iii) f (x) = x, x is a real number.
The function ‘t’ which maps temperature in degree Celsius into temperature in
degree Fahrenheit is defined by t(C) =
9C
5
+ 32.
Find (i) t(0) (ii) t(28) (iii) t(–10) (iv) The value of C, when t(C) = 212.
A function f is defined by f(x) = 2x –5. Write down the values of
(i) f (0), (ii) f (7), (iii) f (–3).
Find the domain and range of the following real functions:
(i) f(x) = – x (ii) f(x) = 2
9
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