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Question

# If f:R→R defined by f(x)={2x+5, x>03x−2, x≤0 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 functionf:R→R f(x)={2x+5, x>03x−2, x≤0 ⇒f′(x)={2, x>03, x≤0 ∵f′(x)>0 ∀x∈R 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)=3x−2 for x≤0 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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