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Let f: R → R be given by f(x) = (x - m)/(x - n), where m and n are distinct real numbers. Then

1. f is injective but not surjective
2. f is injective and surjective
3. f is not injective but surjective
4. f is neither injective nor surjective

Correct answer: f is injective but not surjective

Solution

The function f(x) = (x - m)/(x - n) is injective because it is a rational function with a unique output for each input, as long as x is not equal to n (where it is undefined). However, it is not surjective because it cannot take the value 1, which is the horizontal asymptote as x approaches infinity.

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