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Question

f:(,)(,) is defined by f(x)=ax+b; a,bR(a0) then f is

A
injective but not surjective
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B
surjective but not injective
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C
bijective
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D
neither injective nor surjective
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Solution

The correct option is D bijective
f(x)=ax+b
f(x)=a
So f(x) is increasing if a>0 or f(x) is decreasing if a<0.
And f(x) lies in the interal (,) in its domain.
So f(x) is monotonic & onto, that is, it is bijective

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