Question

Domain of $f\left(x\right)=\frac{x^2+3x+5}{x^2-5x+4}$ is

Answer 1

To find domain.

equate denominator $x^2-5x+4$ to zero. and find the value of x.

$x^2-5x+4=0$

$x^2-4x-x+4=0$

$x(x-4)-1(x-4)=0$

$(x-1)(x-4)=0$

$x=1,4$

This means that, when $x=$1 or 4, we have the $x^2-5x+4$ Implying that

$f\left(x\right)=\frac{x^2+3x+5}{0}$ which is undifined .

so , Domain of function =$R-$ {1,4}.