consider the relation R=[(1,2),(2,5),(3.10),(4,17),(5,26)]. find the

i)range ii)domain iii)inverse

Assuming the relation is

f(x)=y=x2+1 where x ∈ ℕ (i.e. x is a member of natural numbers), then the domain is
{x:[1,5] ∈ ℕ}
Range is
{y:[2,26] ∈ ℕ}
Inverse:
f-1(y) = sqrt((y-1)) : f-1(y)>0

Correction for range, which is the set of all values produced by the function within the given domain. For the above relation

f(x)=y=x2+1,
the domain is
{1,2,3,4,5}
the range is
{2,5,10,17,26}
The inverse is as above.

To find the range, domain, and inverse of a given relation, you can follow these steps:

1) Range: The range of a relation is the set of all possible output values. In this case, the relation is given as R = [(1,2),(2,5),(3,10),(4,17),(5,26)]. To find the range, you need to collect all the second elements (y-values) from each ordered pair in the relation. So, the range is {2, 5, 10, 17, 26}.

2) Domain: The domain of a relation is the set of all possible input values. In this case, you need to collect all the first elements (x-values) from each ordered pair in the relation. So, the domain is {1, 2, 3, 4, 5}.

3) Inverse: To find the inverse of a relation, you need to interchange the first and second elements (x and y values) in each ordered pair. So, the inverse of relation R will be [(2, 1), (5, 2), (10, 3), (17, 4), (26, 5)].

Therefore,
i) The range of R is {2, 5, 10, 17, 26}.
ii) The domain of R is {1, 2, 3, 4, 5}.
iii) The inverse of R is [(2, 1), (5, 2), (10, 3), (17, 4), (26, 5)].