Question

write the domain of F(x)=(x)2-2x+3/(x)2-x-20​

Answer 1

$f(x) = \frac{ {x}^{2} - 2x + 3}{ {x}^{2} - x - 20 }$

Here,

${x}^{2} - 2x + 3 > 0$

So, function is dependent only on its denominator for its changing values.

And, now The roots of the denominator are

$( {x}^{2} - x - 20) = 0$

$(x - 5)(x + 4) = 0$

$x = - 4 \: and \: 5$

Therefore, the domain is

$x ∈ ( - \infty, - 4) ∪ ( - 4,5) ∪ (5 , \infty )$