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| 1. |
Find domain of 9-x^ |
| Answer» {tex}f(x) = \\sqrt {9 - {x^2}} {/tex}The function is not defined when 9 - x2 < 0{tex}\\therefore {/tex}\xa0Domain of function {tex}=\\{ x:9 - {x^2} \\geqslant 0\\} = \\{ x:{x^2} - 9 \\leqslant 0\\} {/tex}{tex} = \\{ x:(x + 3)(x - 3) \\leqslant 0\\} {/tex}= [-3, 3]Now {tex}f(x) = \\sqrt {9 - {x^2}} \\geqslant 0{/tex}\xa0for {tex}x \\in [ - 3,3]{/tex}{tex}\\therefore {/tex}\xa0Range of function =\xa0{tex}\\left[ {0,\\infty } \\right){/tex} | |