Q. 3 H4.6( 5 Votes )

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


Answer :


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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