Question

g(x)=x^2 +3x -40
f(x)= x^2 +5x+6

find the values of x that are NOT in the domain of the function g/f

Answer 1

Factor f(x)

\(f(x) = x^2 + 5x + 6 =(x+2)(x+3)\)
You could factor the numerator if you want, but it's not necessary. You'll only encounter problems with the denominator.
\[\frac{g(x)}{f(x)}=\frac{x^2+3x-40}{(x+2)(x+3)} \]
Any value of \(x\) is valid to use, except for cases that produces a denominator of 0 (because you can't divide by 0). So what numbers make the denominator 0?
\((x+2)(x+3)=0\)... you can get zero if \((x+2)=0\) or if \((x+3)=0\), meaning \(x=-2\) or \(x=-3\)... so the values that CANNOT be in the domain are -2 and -3