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Question

If f:[1,)[0,) and f(x)=x1+x then f is


A
one-one and into
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B
onto but not one-one
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C
one-one and onto
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D
neither one-one nor onto
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Solution

The correct option is A one-one and into

Given that f:[0,)[0,)
s.t.f(x)=xx+1
then f(x)=1+xx(1+x2)=1(1+x)2 >0,x
f is an increasing function is one-one.
Also Df=[0,)
And for range let xx+1=yx=yy+1


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