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)=(3x-2)/(x+2)`
Answer» Correct Answer - dom `(f)=R-{-2}," range "(f)=R-{3}` `f(x)=(3x-2)/(x+2)` not defined when x=-2. So, dom `(f)=R-{-2}`. Let y=f(x). Then, `y=(3 x-2)/(x+2)impliesxy+2y=3x-2implies3x-xy=2y+2` `impliesx(3-y)=2y+2impliesx=(2y+2)/(3-y)." "....(i)` It follows from (i) that x is not defined when y=3. `:." range "(f)=R-{3}`.

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