InterviewSolution
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InterviewSolution
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Let `A=" "{1,2,3,4,5," "6," "7," "8," "9," "10}`and `B" "=" "{" "2,3,5,7" "}dot`Find `A nnB`and hence show that `A nnB" "=" "Bdot` |
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Answer» Here `f:[0,oo)toR:f(x)=sqrtxandg:[0,oo)toR:g(x)=x`. `:."dom "(f)=[0,oo)" and dom "(g)=[0,oo)` So, dom `(f)nn" dom "(g)=[0,oo)nn[0,oo)=[0,oo)`. (i) `(f+g):[0,oo)toR` is given by `(f+g)(x)=f(x)+g(x)=(sqrtx+x)`. (ii) `(f-g):[0,oo)toR` is given by `(f-g)(x)=f(x)-g(x)=(sqrtx-x)`. (iii) `(fg):[0,oo)toR` is given by `(fg)(x)=f(x).g(x)=(sqrtx""xxx)=x^(3//2)` (iv) `{x:g(x)=0}={0}`. `:."dom "((f)/(g))=" dom "(f)nn"dom "(g)-{x:g(x)=0}` `=[0,oo)nn[0,oo)-{0}=(0 ,oo)`. So, `(f)/(g):(0,oo)toR` is given by `((f)/(g))(x)=(f(x))/(g(x))=(sqrtx)/(x)=(1)/(sqrtx),xne0`. |
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