Solution to Let A = {a,b,c,d} and B = {c,d,e,f,g}. Let R1 = {(a,c), (b,d), (c,e)} R2 … - Sikademy
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Archangel Macsika

Let A = {a,b,c,d} and B = {c,d,e,f,g}. Let R1 = {(a,c), (b,d), (c,e)} R2 = {(a,c), (a,g), (b,d), (c,e), (d,f)} R3 = {(a,c), (b,d), (c,e), (d,f)} Justify which of the given relation is a function from A to B. (c) Let f be a real valued function defined by f(x) = 1 x2−9 . (i) What is the domain of f? (ii) What is the range of f? (iii) Represent f as a set of ordered pairs.

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Given A = \{a,b,c,d\} and B = \{c,d,e,f,g\} .

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)\}

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 R_3 is a function.

(c) Given f is a real valued function defined by f(x) = x^2 - 9 .

(I) Function is defined for all real values of x. Hence,

Domain off = \R

(ii) Now, as x^2 \geq 0 \implies x^2-9 \geq -9

Hence, Range of f = [-9,\infin)

(iii) Representation of f as a set of ordered pair = \{ (x,x^2-9) : x \in \R\}

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