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Let f:RtoR be a function defined as f(x)...

Let `f:RtoR` be a function defined as `f(x)=x|x|,` for each `x""inR,R` being the set of real numbers. Which one of the following is correct?

A

f is one -one but not onto

B

f is onto but not one-one

C

f is both one-one and onto

D

f is neither one-one nor onto

Text Solution

Verified by Experts

The correct Answer is:
C
Given, `f(x)=x|x|`
If `f(x_(1))=f(x_(2))`
`impliesx_(1)|x_(1)|=x_(2)|x_(2)|`
`impliesx_(1)=x_(2)`
`:.` f(x) is one-one.
Also, range of f(x)=co-domain of f(x)
`:.f(x)` is onto.
Hence, f(x) is both one-one and onto.
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