Question

Determine the domain of the function (f o g)(x) where f(x)= 3/x+2 and g=5/x.

Since it's a composite function, do I solve it by setting it up as 3/x+2/5/x? If so, what are the steps to solving that kind of complex division? Or should I be doing some sort of multiplication because they're both fractions?

Answer 1

The Domain is all real values of x except x = 0 and x = -2.5.

Explanation:

I am assuming that f(x) = 3/(x + 2).

(f o g)x is found by substituting 5/x for the x in 3/(x + 2).

(f o g) x = 3/ ( 5/x + 2)

= 3 / ( 5+2x) / x

= 3x / (5 + 2x).

When finding the domain you first check for values of x which make g(x) undefined then values of x which make (f o g)(x) undefined.

x = 0 makes g(x) = 5/0 so it is undefined and x = -2.5 makes g o f undefined also.