Question

Hello, May I please get some assistance with this homework question? I posted an image below Q2

Answer 1

Solving (a)

The two functions we have are:

$\begin{gathered} f(x)=3x+3 \\ g(x)=x^2 \end{gathered}$

We are asked to find the composite function:

$(f\circ g)(x)$

Step 1. The definition of a composite function is:

$(h\circ k)(x)=h(k(x))$

In this case:

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

This means to plug the g(x) expression into the value of x of the f(x) function.

Step 2. Substituitng g(x) as the value for x in f(x):

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

Simplifying:

$(f\circ g)(x)=\boxed{4x^2+3}$

Step 3. We also need to find the domain of this composite function.

The domain of a function is the possible values that the x-variable can take. In this case, there would be no issues with any x value that we plug as the x-value. Therefore, the domain is all real numbers.

The domain of fog is all real numbers.

Answer:

$(f\circ g)(x)=\boxed{4x^2+3}$

The domain of fog is all real numbers.