Question

Define : $f\left(x\right)=\frac{1}{6x-x^2-5}$

Answer 1

$f\left(x\right)=\frac{1}{6x-x^2-5}=-\frac{1}{(x-5)(x-1)}\Rightarrow f\left(x\right)=-\frac{1}{(x-5)(x-1)}f\left(x\right)\to +ve,1<x<5f\left(x\right)=0,x=1,5f\left(x\right)\to -ve,x>5,x<1$