InterviewSolution
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InterviewSolution
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Find the domain and range of the real function `f(x) = sqrt(9 -x^(2))` |
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Answer» If its clear that f(x) `= sqrt(9-x^(2))` is not defined when `(9-x^(2)) lt 0, i.e.,` When `x^(2) gt 9 , i.e., " when " x gt 3 " or " x lt -3` `:. " don " (f) ={ x in R : -3 le x le 3}` Also `y= sqrt(9 - x^(2)) rArr y^(2) = (9 -x^(2))` ` rArr x= sqrt(9 -y^(2))` Clearly x is not defined when `(9-y^(2)) lt 0` But `(9-y^(2)) lt 0 rArr y^(2) gt 9` `rArr y gt 3 " or " y lt -3` `:.` range `(f) ={ y in R : - 3 le y le 3}` |
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