Let the function `f: R-{-b}->R-{1}` be defined by `f(x)=(x+a)/(x+b)` , `a!=b` , then (a) `f` is one-one but not onto (b) `f` is onto but not one-one (c) `f` is both one-one and onto (d) none of these

Explanation

Let `x, y` be two numbers in set `R-{-b}` such that `f(x)=f(y)`



`therefore frac{{x}+{a}}{{x}+{b}}=frac{{y}+{a}}{{y}+{b}} text {. }`



Simplifying the equation we get



`a y+b x=a x+b y `


`therefore y(a-b)=x(a-b) `


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