Question

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 1

(a) f is one-one onto.

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f : R → R is defined by f(x) = 3x.

(a) f(x1) = 3x1, f(x2) = 3x2

f(x1) = f(x2)

⇒ f is one-one.

(b) For every member y belonging to co-domain has pre-image x in domain of f.

Since y = 3x, ⇒ x = \(\frac{y}{3}\)

∴ f is onto.

∴ f is one-one and onto.