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Question

If f:RR defined by f(x)={2x+5, x>03x2, x0 then f is

A
many-one function
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B
one-one function
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C
onto function
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D
into function
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Solution

The correct option is D into function
f:RR
f(x)={2x+5, x>03x2, x0
f(x)={2, x>03, x0
f(x)>0 xR
So, f is strictly increasing function
Therefore, f is one-one function.
Now,
When f(x)=2x+5 for x>0 its range lies from (5,).
Similarly when f(x)=3x2 for x0 its range lies from (,2].
So,Range of f(x)=(,2](5,)
f(x) is not onto function because the function range is not equal to its co-domain.

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