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Let f : R->Rbe defined as f(x) = 3x. Ch...

Let `f : R->R`be defined as `f(x) = 3x`. Choose the correct answer.
(A) f is one-one onto
(B) f is many-one onto
(C) f is one-one but not onto
(D) f is neither one-one nor onto.

Text Solution

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`f : R to R ` is define d as `f(x)=3x`
Let `x,y in R` such that `f(x)=f(y)`
`implies 3x=3y`
`implies x=y`
`f ` is one-one.
Also, for any real number,`(y)` in co domain `R` there exists `y/3` in `R` such that `f(y/3)=3(y/3)=y`
`f` is onto.
Hence function is one one and onto.
The correct answer is A.
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