Question

Find the domains of ( f o g)(x) and ( g o f)(x)

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

Answer 1

(f o g)(x) is the "composition" of functions f and g. Have you found compositions before? If so, recall that function g(x) becomes the input to function f(x).

Write out this composition first. If your work is correct, we'll then focus on finding the domain of (f o g)(x).

Answer 2

yea i learned that ( f o g)(x) is the same thing as f(x)+g(x) but im not quite sure how to apply that to this problem

Answer 3

5x/x-5+x-4/x+4= 5x(x+4)/(x-5)(x+4)-4(x-5/(x+4)(x-5) ?

Answer 4

No, No! (f o g)(x) is definitelyl not the same as f(x) + g(x).

Better go back and review "composite functions," as well as "sums and differences of functions.

Answer 5

Ohh ok i think i get it, for the first one i got it can be all values except -6 and for the second 1 i got it can be all values but 20/9

Answer 6

so could I write it as:
1. (-∞,-5]U(-6,∞)
2. (-∞,-20/9)U(-20/9,∞)
@mathmale