Respuesta :
The composite function [tex] (g \circle h)(x) [/tex] works like this:
- Take a number [tex] x [/tex] as input
- Evaluate h(x) = 3x. Let's call this output z.
- Evaluate g(x) = 1/(z+2)
So, if we substitute back z = 3x, the final output is 1/(3x+2). We know that the denominator of a fraction can't be zero, so we must impose
[tex] 3x+2 \neq 0 \iff 3x \neq -2 \iff x \neq -\dfrac{2}{3} [/tex]
