Question

Let $f:R\to R$ be defined as f(x)=3x. Choose the correct answer.
(a)f is one-one onto
(b)f is many -one onto
(c) f in one-one but not onto
(d) f is neither one-one nor onto

Answer 1

$f:R\to R$ is defined as f(x)=3x
Let $x,y\in R$ such that f(x)=f(y).
$\Rightarrow 3x=3y\Rightarrow x=y$
Therefore, f is one-one.
Also, for any real number (y)in co-domain R, there exists $\frac{y}{3}$ in R such that $f\left(\frac{y}{3}\right)=3\left(\frac{y}{3}\right)=y$
Therefore, f is onto. Hence, function f is one-one and onto.
The correct answer is (a)