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  2. 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.
# NCERT

Q.12 Letf : R\rightarrow R be defined asf(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.

Answers (1)
S seema garhwal

f : R\rightarrow R

f(x) = 3x

One - One :

Let \left ( x,y \right ) \in R

             f(x)=f(y)

                  3x=3y

                  x=y

       \therefore  f is one-one.

 

Onto:

We have  y \in R, then there exists x=\frac{y}{3} \in R    such that 

f(\frac{y}{3})= 3\times \frac{y}{3} = y             

\therefore f is \, \, onto.

Hence, the function is one-one and onto.

The correct answer is A .

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