Composite functions

Composite
functions

Suppose that

We are going to evaluate one of these functions with the other function:

We read this as f of g of x

What about

We read this as g of f of x

Math Response

Let $$f\left(x\right)=12x+4$$ and $$g\left(x\right)=-x^2-4$$ .

Compute

$$f\left[g\left(x\right)\right]=$$

Give your answer in its most simple form.

Type answer here

Correct Answer: -12x^2-44

Deg^°

Rad

Evaluating a composite function

Now suppose that

Now we want to find

Math Response

Let $$f\left(x\right)=-6x+8$$ and $$g\left(x\right)=2x^3+x$$ ,

find

$$f\left[g\left(3\right)\right]=$$

Type answer here

Correct Answer: -334

Deg^°

Rad

We will see a way to compose functions given their graphs tomorrow.