227k views
0 votes
Hello, May I please get some assistance with this homework question? I posted an image below Q2

Hello, May I please get some assistance with this homework question? I posted an image-example-1

1 Answer

4 votes

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.

User Talouv
by
8.5k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories