Find the range of each of the following functions.
f(x) = x2 + 2, x, is a real number.
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
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`)
Let x be any real number.
x2 ≥ 0
⇒ x2 + 2 ≥ 0 + 2
⇒ x2 + 2 ≥ 2
⇒ f(x) ≥ 2
∴ Range of f = [2, `oo`)
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