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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:
Let x1, x2 ∈ R such that f(x1) = f(x2)
⇒ 3x1 = 3x2
⇒ x1 = x2
∴ f is one-one.
Consider any y ∈ R (co-domain of f); there exist x ∈ R (domain of f) such that:
f(x) = y
⇒ 3x = y
⇒ x = `y/3`
∴ `f(y/3) = 3.y/3` = y
∴ f is onto.
Hence, f is one-one onto.
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