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Find the domain and range of of square root x minus one into 3 - x |
| Answer» We have,f(x)=(x−1)(3−x)\u200bNow,Under square root the polynomial must be positive. The domain is obtained by solving:-(x−1)(3−x)≥0You can obtain the zeroes of the polynomial(x−1)(3−x)=0Ifx−1=0x=1If3−x=0⇒x=3So,x=1,3So the polynomial is solved in the external intervals.x>1,x>3So,x∈(1,+∞)Since the function\xa0f(x)\xa0is positive, due to result of square root,The range includes all positive real numbers\xa0x≥0Hence, this is the answer. | |