Here's the Solution to this Question
Given A [tex]= \{a,b,c,d\}A={a,b,c,d} and B = \{c,d,e,f,g\}B={c,d,e,f,g} .[/tex]
[tex]R_1 = \{(a,c), (b,d), (c,e)\}, R_2 = \{(a,c), (a,g), (b,d), (c,e), (d,f)\}, \\ R_3 = \{(a,c), (b,d), (c,e), (d,f)\}[/tex]
A relation is a function when every element of set A has image in B and a element of set A can-not have more than one image in set B.
So, Relation [tex]R_3[/tex] is a function.
(c) Given [tex]f[/tex] is a real valued function defined by [tex]f(x) = x^2 - 9[/tex].
(I) Function is defined for all real values of [tex]x[/tex]. Hence,
Domain of [tex]f=R[/tex]
(ii) Now, as [tex]x^2 \geq 0[/tex] [tex]\implies[/tex] [tex]x^2-9 \geq -9x[/tex]
Hence, Range of f=[−9,∞)
(iii) Representation of [tex]f[/tex] as a set of ordered pair = [tex]\{ (x,x^2-9) : x \in R\}[/tex]
