Question

1) F(x)= (X+2)/(X^2-4x-5)
A) Find the domain (-00,-1)u(-1,5)u(5,00)
B) find F(-3) I'm not sure how to do it.
C) Find F(X+2) I'm not sure either.

2. f(x)= (2x)/(x-4) G(x)= (x)/(X+5) find the domain of each.

A)(F+G) (4x^2+5x)(x-4)(X+5) x can't= 4,-5

B) (F*G) (2x^2)/(x-4)(x+5) domain is the same

C) (F/g) (2x^2)+5/x(x-4) Not sure how to interpret domain.

Answer 1

1B
Just plug in -3 for x.
F(-3) = (-3+2)/((-3)^2-4(-3)-5) = -1/16
1C
F(x+2) = ((x+2)+2)/((x+2)^2-4(x+2)-5) = (x+4)/(x^2-9)

2A
I get 3x(x+2) / (x-4)(x+5)
your domain is correct, however

2B ok

2C
f/g = 2(x+5) / (x-4)

So, it looks like the domain is all reals except x=4, but you have to remember that

g(x) is not defined for x = -5, so f/g is not defined.

g(x)=0 for x=0, so f/g is not defined there either

So, the domain is all reals except -5,0,4