Let `f:R^+ -> R` is a function defined as `f(x) = log x`. Find (i) Ima – InterviewSolution

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1.	Let `f:R^+ -> R` is a function defined as `f(x) = log x`. Find (i) Image of domain of `f`, (ii) `(x: f(x)=-2)` (iii) `f(xy) = f(x) + f(y)`
Answer» Correct Answer - (i) R (ii) `{e^(-2)}` (iii) Yes (i) For every `x""inR^(+)`, we have `log_(e)x=R`. So, range (f)=R. (ii) `f(x)=-2implieslog_(e)x=-2x=e^(-2)`. So, `{x:x""inR^(+)andf(x)=-2}={e^(-2)}`. (iii) `f(xy)=log_(e)(xy)=log_(e)xy=f(x)+f(y)`.

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