Answer:
(f/g)(x) = [tex]\frac{2x^2-5}{3x+2}[/tex] x can not equal -2/3
Step-by-step explanation:
(f / g) is telling you to make f the numerator and g as the denominator.
It also wants you to state the domain restriction. When you divide by something, remember you can not divide by 0 under any circumstances. This means, you need to find what combination of x values will result in the denominator equaling 0.
(f / g) (x)
[tex]\frac{2x^2-5}{3x+2}[/tex]
Domain restrictions
As you can see here, our denominator is: 3x+2. What set of x values will result in 3x+2 equating to zero? To find this, set up the equation so that it equals zero.
[tex]3x+2=0\\3x+2-2=0-2\\3x=-2\\3x/3=-2/3\\x=-\frac{2}{3}[/tex]
If you are not sure, replace x with the value you came up with.
To check, replace x with -2/3
[tex]3(-\frac{2}{3})+2=0\\-2+2=0\\0=0[/tex]
