Let f : R → R be defined as f ( x ) = 3 x . 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

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Solution

The given function f:R→R is defined by f( x )=3x.

Let x,y∈R such that, f( x )=f( y ).

⇒3x=3y ⇒x=y

So, f( x )=f( y ) implies, x=y.

Therefore, f is one-one.

For y∈R, there exists y 3 in R such that,

f( y 3 )=3( y 3 ) =y

So, f is onto.

Thus, function f:R→R , defined by f( x )=3x. is both one-one and onto.

Thus, option (A) is correct.

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