If $f$ is a relation from set of positive real number to the set of positive real numbers defined by $f(x)=3…
If $f$ is a relation from set of positive real number to the set of positive real numbers defined by $f(x)=3 x^2-2$, then $f$ is
one-one but not onto
onto but not one-one
a bijection
not a function
Solution
(w) $f: R_{+} \rightarrow R_{+}$
$
f(x)=3 x^2-2
$
As
$
\begin{aligned}
& x \in(0, \infty) \\
& 3 x^2-2 \in(-2, \infty)
\end{aligned}
$
But co-domain of $f$ is $R_{+}$.
Hence, $f$ is not a function