Question

solve for domain of $f\left(x\right)=\frac{1}{6x-x^2-5}$

Answer 1

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

For $f\left(x\right)$ to be defined

$6x-x^2-5\ne 0$

$x^2-6x+5\ne 0$

$x^2-5x-x+5\ne 0$

$x(x-5)-1(x-5)\ne 0$

$(x-1)(x-5)\ne 0$

$x\ne 1,5$

$x\in R-\{1,5\}$.