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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.

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

Verified by Experts

The correct Answer is:
A
In `f : R to R " " f(x) = 3x`
Let `x, y in R `
and `f(x) = f(y)`
`rArr 3x = 3y " " rArr x=y`
`therefore f` is one-one.
Again let `f(x)= y ` where `y in R`
`rArr " " 3x =y`
`rArr " "x = (y)/(3) in R`
`therefore f` is onto.
Therefore, `f` is one-one onto.
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