InterviewSolution
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InterviewSolution
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Find the domain of each of the following real fuctions: (i) `f(x)=sqrt(x-3)` (ii) `g(x)=sqrt(4-x^(2))` (iii) `h(x)=(1)/(sqrt(1-x))`. |
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Answer» (i) We have, `f(x)=sqrt(x-3)`. Clearly, f(x) is defined for all real values of x for which `x-3ge0,i.e.,xge3`. `:."dom "(f)=[3,oo)`. (ii) We have, `g(x) =sqrt(4-x^(2))` Clearly, g(x) is defined for all real values of x for which `(4-x^(2))ge0` But, `(4-x^(2))ge0implies-(4-x^(2))le0` `impliesx^(2)-4le0implies(x+2)(x-2)le0` `implies-2lexle2impliesx""in[-2,2]`. `:."dom "(g)=[-2,2]`. (iii) We have, `h(x)=(1)/(sqrt(1-x))` Clearly, h(x) is defined for all real values of x for which `(1-x)gt0`. But, `1-xgt0implies1gtximplieslt1impliesx""in(-oo,1)`. `:."dom "(h)=(-oo,1)`. |
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