Question #129375
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.
1
Expert's answer
2020-08-13T18:33:36-0400

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

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)}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 R3R_3 is a function.


(c) Given ff is a real valued function defined by f(x)=x29f(x) = x^2 - 9 .

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

Domain off=Rf = \R

(ii) Now, as x20    x299x^2 \geq 0 \implies x^2-9 \geq -9

Hence, Range of f=[9,)f = [-9,\infin)

(iii) Representation of ff as a set of ordered pair = {(x,x29):xR}\{ (x,x^2-9) : x \in \R\}


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