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Find the domain and range of …

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Find the domain and range of of square root x minus one into 3 - x

Posted by Shavitaj Kaur 4 years, 7 months ago

CBSE > Class 11 > Mathematics

1 answers

Sanchita Sharma 4 years, 7 months ago

We have, f(x)=(x−1)(3−x) Now, Under square root the polynomial must be positive. The domain is obtained by solving:- (x−1)(3−x)≥0 You can obtain the zeroes of the polynomial (x−1)(3−x)=0 If x−1=0 x=1 If 3−x=0 ⇒x=3 So, x=1,3 So the polynomial is solved in the external intervals. x>1,x>3 So, x∈(1,+∞) Since the function f(x) is positive, due to result of square root, The range includes all positive real numbers x≥0 Hence, this is the answer.

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