Thank you for reporting, we will resolve it shortly
Q.
The range of the function $f ( x )=\frac{ e ^{ x } \ln x 5^{\left( x ^2+2\right)}\left( x ^2-7 x +10\right)}{2 x ^2-11 x +12}$ is
Relations and Functions - Part 2
Solution:
$f(x)=\frac{e^x \ln x 5^{\left(x^2+2\right)} \cdot(x-2)(x-5)}{(2 x-3)(x-4)}$
Note that at $x=3 / 2$ and $x=4$ function is not defined and in open interval $(3 / 2,4)$ function is continuous.
$\underset {x \rightarrow \frac{3}{2}^{+}}{\text{Lim}} =\frac{(+ ve )(- ve )(- ve )}{(+ ve )(- ve )} \rightarrow-\infty$
$\underset{x \rightarrow 4^{-}}{\text{Lim}} =\frac{(+ ve )(+ ve )(- ve )}{(+ ve )(- ve )} \rightarrow \infty$
In the open interval $(3 / 2,4)$ the function is continuous and takes up all real values from $(-\infty, \infty)$ Hence range of the function is $(-\infty, \infty)$ or $R$