Question

Find the domain of the composite function g(f(x)).
F(x)= x+6, G(y)= 2/y
G(f(x))= 2/x+6

Answer 1

You can't have 0 in the denominator. What value of x gives you a zero in the denominator?

Answer 2

the domain includes all the values that do not make the denominator zero so it must be everywhere where x cannot be -6

Answer 3

so all real values except zero is the answer?

Answer 4

no the denominator cannot equal zero, in this functino what is your denominator?

Answer 5

in the first part it's y, and in the second part its x+6

Answer 6

so everywhere where that doesnt equal zero is the domain (for x)

Answer 7

so the domain of x is everywhere but x=-6 or y=0

Answer 8

but since its g(f(x)) it is just everywhere but x=-6