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Question
Let f : R → R be defined as f(x) = 3x. Choose the correct answer.
Options
f is one-one onto.
f is many-one onto.
f is one-one but not onto.
f is neither one-one nor onto.
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Solution
f is one-one onto.
Explanation:
f : R → R is defined as f(x) = 3x.
Let x, y ∈ 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 `y/3` in R such that `f(y/3) = 3(y/3) = y`.
∴ f is onto.
Hence, function f is one-one and onto.
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