Find the domain and range of the following functions To give

Find the domain and range of the following functions. To give yourself a hint, try to write up f-values for some x-s first (take specific x and find what fix) would be). The function that assigns to each non-negative integer its last digit. Domain: Range: f(x) = 1/(1+x^2) Domain: Range:

Solution

a) Domain : (0, Infinity) because it takes non-negative(positive number) as input.

Range : (11, Infinity) because adding last digit will result in positive number. Smallest number in domain is 1, and it\'s output would be 11. So minimum value is 11.

b) Domain : x^2 is always positive, so domain would be (-Infinity, +Infinity)

Range : For x = 0, f(0) = 1. For any x other than 0, denominator would be > 1, and hence f(x) < 1

(0,1)