Answer 1

f(x) = x² + 2, x, is a real number

The values of f(x) for various values of real numbers x can be written in the tabular form as

x	0	±0.3	±0.8	±1	±2	±3	...
f(x)	2	2.09	2.64	3	6	11	...

Thus, it can be clearly observed that the range of f is the set of all real numbers greater than 2.

i.e., range of f = [2,`oo`)

Alter:

Let x be any real number.

Accordingly,

x² ≥ 0

⇒ x² + 2 ≥ 0 + 2

⇒ x² + 2 ≥ 2

⇒ f(x) ≥ 2

∴ Range of f = [2, `oo`)