InterviewSolution
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InterviewSolution
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The function `f:[0,oo] to R` given by f(x)=(x)/(x+1)` isA. one-one and intoB. one-one but not ontoC. onto but not one-oneD. neither one-one nor onto |
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Answer» Correct Answer - B We have, `f(x)=(x)/(x+1)=1-(1)/(1+x)` Let `x, y in R` be such that `f(x)=f(y)`. Then, f(x)=f(y) `Rightarrow 1-(1)/(1+x)=1-(1)/(1+y)Rightarrow 1+x=1+y Rightarrow x=y` `therefore ` f is one-one Clearly, f is not onto as f takes only values less than 1 i.e. Range `f=(-oo, 1) ne` co-domain of f. |
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