We know that [tex]f(x)=3x+1[/tex] and [tex]g(x)=x^2-6[/tex]; to find [tex]( \frac{g}{f} )(x)[/tex] we are going to divide [tex]g(x)[/tex] by [tex]f(x)[/tex]:
[tex]( \frac{g}{f} )(x)= \frac{x^2-6}{3x+1} [/tex]
Since the denoinatorcan't be zero:
[tex]3x+1 \neq 0[/tex]
[tex]x \neq - \frac{1}{3} [/tex]
We can conclude that the correct answer is A. [tex]\frac{x^2-6}{3x+1} [/tex] [tex]x \neq - \frac{1}{3}[/tex]
