Let the function `f:R -(-b) to r-(-1)` is defined by `(x+a)/(x+b)=(y+a – InterviewSolution

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1.	Let the function `f:R -(-b) to r-(-1)` is defined by `(x+a)/(x+b)=(y+a)/(y+b)`, thenA. f is one-one but not ontoB. f is onto but not one-oneC. f is both one-one and ontoD. None of these
Answer» Correct Answer - C `Rightarrow (x+a)/(x+b)=(y+a)/(y+b) Rightarrow 1+(a-b)/(x+b)=1+(a-b)/(a+b) Rightarrow x=y` So, if one-one Let `y in R` such that f(x)=y. Then. `f(x)=y Rightarrow (x+a)/(x+b)=y Rightarrow x=(a-by)/(y-1)` `"Clearly", x in R -(-b)"for all "y in R -(-1).So, Hence, f is both one-one and onto.

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