--->Question:

f(x) = sqrt(4*x+5)

g(x) = (x-2)/x

find g/f(x) and it's domain

--->My Answer:

-find domain for both f(x) and g(x)

f(x)-- sqrt(4*x+5) ---- under square root has to be greater than or = to zero

4x+5 >= 0

4x >= -5

x >= -5/4

g(x) -- the denominator cannot be zero

x =! 0

so for (g/f)(x), g has to be defined, f has to be defined and f can't be zero

((x-2)/x) * (1/(sqrt(4x+5)))

x =! 0 & x > -5/4 [[[[no longer greater than or equal to 0]]]]]

so domain in interval notation is

(-5/4,0)U(0,infinity)

DID I DO THIS RIGHT!?!?

thanks for your help