Question

What is the range when f is given as ordered pairs?

Answer 1

Here's the Solution to this Question

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

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

Hence, Range of f=[−9,∞)

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