Respuesta :
Answer:
The function is [tex]\left(f \circ g \right) \left( x \right) = - 30 x - 21[/tex] and the domain is all real numbers.
Step-by-step explanation:
Composition of functions is when one function is inside of another function.
The notation used for the composition of functions looks like this, [tex]\left(f \circ g \right) \left( x \right) = f(g(x))[/tex].
We have the following functions
[tex]f(x)= -6x + 3\\\\g(x) = 5x + 4[/tex]
The composite function is
[tex]\left(f \circ g \right) \left( x \right) = f \left( g \left( x \right) \right)=f \left(5 x + 4 \right) = 3 - 6 {\left(5 x + 4\right)} = - 30 x - 21[/tex].
The domain is the set of all possible x-values which will make the function "work", and will output real y-values.
The function [tex]\left(f \circ g \right) \left( x \right) = - 30 x - 21[/tex] has no undefined points nor domain constraints. Therefore, the domain is [tex]-\infty \:<x<\infty \:[/tex] or all real numbers.
