# Find The Range of Each of the Following Functions. F(X) = X2 + 2, X, is a Real Number. - Mathematics

Sum

Find the range of each of the following functions.

f(x) = x2 + 2, x, is a real number.

#### Solution

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)

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#### APPEARS IN

NCERT Class 11 Mathematics Textbook
Chapter 2 Relations and Functions
Exercise 2.3 | Q 5.2 | Page 44