Answer:
[tex](g\circ f)(x)=30x-9,\text{Domain:(}-\infty,\infty)[/tex]
Explanation:
Given the functions f(x) and g(x) defined as follows:
[tex]\begin{gathered} f\mleft(x\mright)=10x-5 \\ g\mleft(x\mright)=3x+6 \end{gathered}[/tex]
The composite function g o f is defined below:
[tex]\begin{gathered} (g\circ f)(x)=g(f(x)) \\ =3f(x)+6 \\ =3(10x-5)+6 \\ =30x-15+6 \\ (g\circ f)(x)=30x-9 \end{gathered}[/tex]
The domain of the function is the set of all possible values of x.
In the composite function, x can take on any value in the real line. Therefore:
[tex]\text{Domain:(}-\infty,\infty)[/tex]
