Question

Find the domain of the function f defined by $f\left(x\right)=\frac{1}{\sqrt{5x-x^2-6}}$.

Answer 1

Given the function $f\left(x\right)=\frac{1}{\sqrt{5x-x^2-6}}$.

Now the function $f\left(x\right)$ is defined for

$5x-x^2-6>0$

or, $x^2-5x+6<0$

or, $(x-3)(x-2)<0$

or, $2<x<3$.

Sot he domain is $(2,3)$.