Find the domain of the range of each of the following real functions: – InterviewSolution

InterviewSolution

1.	Find the domain of the range of each of the following real functions: `f(x)=(1)/(sqrt(2x-3))`
Answer» Correct Answer - dom `(f)=R-(-oo,(3)/(2))," range "(f)=R-{0}` `f(x)=(1)/(sqrt(2x-3))` is not defined when `2x-3le0` i.e., when `xle(3)/(2)`. `:."dom "(f)=R-(-oo,(3)/(2)]`. Let y=f(x). Then, `y=(1)/(sqrt(2x-3))impliesy^(2)=(1)/((2x-3))implies(2x-3)=(1)/(y^(2))impliesx=(1)/(2)((1)/(y^(2))+3)`. `:.` x is not defined when y=0. So, range `(f)=R-{0}`.

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