ANSWER
• (g o f)(x) = ,16x² + 24x + 9
,
• B., the domain of g o f is all real numbers
EXPLANATION
The composition is,
[tex](g\circ f)(x)=g(f(x))[/tex]
This means that, to find the composition, we have to replace x with f(x) in the function g(x),
[tex]g(f(x))=(f(x))^2[/tex]
Now, replace f(x) with its expression,
[tex]g(f(x))=(4x+3)^2[/tex]
We can expand this binomial squared to write it in standard form. The composition is,
[tex](g\circ f)(x)=16x^2+24x+9[/tex]
As we can see, this is a polynomial function. Therefore, the domain is all real numbers.
