Question

Determine the domain of (f/g)(x) when f(x) = 1/x and g(x) = sqrt(x+5).

I have the domains of both functions and I know how to set up (f/g)(x), but I don't know where to go from there.

(f/g)(x)= (1/x)/(sqrt(x+5))
domain of f(x) = (-∞,0)-(0,∞)
domain of g(x) = (-5,∞)

Answer 1

[1/x] / sqrt(x+5) yes =
= 1 /[ x sqrt(x+5) ]
that excludes x = 0 and x = -5 from the domain
-oo to -5
-5 to 0
0 to +oo

Answer 2

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