Question

Define a relation R from R to R as follows: For all (x, y) E R x R, (x, y) E R if, and only if, x= y2 + 1. (a) Is (2, 5) E R? Is (5, 2) e R? Is (-3) R 10? Is 10 R (-3)? (b) Draw the graph of R in the Cartesian plane. (C) Is R a function from R to R? Explain.

Answer 1

a) Since

$2 \neq 5^2+1$

so

(2.5)

doesn't belong to

Since

5=22+1

so

belongs to

Since

$-3\neq 10^2+1,$

so

doesn't hold.

Since

$10=(-3)^2+1,$

so

holds.

b) c) Since

5 10 -5 0 5 -5

and

belong to

therefore

is not a function from

$\mathbb{R}$ to $\mathbb{R}.$