Q. 124.3( 19 Votes )

# 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.

Answer :

It is given that f: R → R be defined as f (x) = 3x.

Let x, y ϵ R such that f(x) = f(y).

⇒ 3x = 3y

⇒ x = y

⇒ f is one–one.

Also, for any real number (y) in co–domain R, there exists in R such that

Therefore, f is onto.

Therefore, function f is one-one and onto.

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