Question

Hello, May I please get some assistance with this homework question? I posted an image below. Question A has already been answered, but do need help with the other questions. Q2 (part b)

Answer 1

ANSWER

• (g o f)(x) = ,16x² + 24x + 9

,

• B., the domain of g o f is all real numbers

EXPLANATION

The composition is,

$(g\circ f)(x)=g(f(x))$

This means that, to find the composition, we have to replace x with f(x) in the function g(x),

$g(f(x))=(f(x))^2$

Now, replace f(x) with its expression,

$g(f(x))=(4x+3)^2$

We can expand this binomial squared to write it in standard form. The composition is,

$(g\circ f)(x)=16x^2+24x+9$

As we can see, this is a polynomial function. Therefore, the domain is all real numbers.