Question

State the domain and range the following functions:

$f\left(x\right)=3x^2-2x+1$

Answer 1

Given, $f\left(x\right)=3x^2-2x+1$
The values of $x$ can be any real number.
Therefore the domain is $x$ belongs to all real numbers.
Observe that $b^2-4ac=4-12=-8<0$. So, the graph is completely above $x$-axis.
Which implies that the range should be greater than than some finite value
$f\left(x\right)\ge \frac{12-4}{12}=\frac{2}{3}$