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

Answer: (A)

f is one-one onto

Answer 2

$f:R→R,f(x)=3x$

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 $\frac{y}{3}$ in R such that $f(\frac{y}{3})=3(\frac{y}{3})=y$.
∴f is onto.
Hence, function f is one-one and onto.
The correct answer is A.