Q. 3 H4.6( 5 Votes )

# Find the domain and range of each of the following real valued functions:

We know the square of a real number is never negative.

Clearly, f(x) takes real values only when 9 – x2 ≥ 0

9 ≥ x2

x2 ≤ 9

x2 – 9 ≤ 0

x2 – 32 ≤ 0

(x + 3)(x – 3) ≤ 0

x ≥ –3 and x ≤ 3

x [–3, 3]

Thus, domain of f = [–3, 3]

When x [–3, 3], we have 0 ≤ 9 – x2 ≤ 9

Hence,

f(x) [0, 3]

Thus, range of f = [0, 3]

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