Question

Given the functions f(x)=3x 2 and g(x)=x²-5, determine the values of the following compositions of the function f(f(-3))

Answer 1

To find the value of the composition f(f(-3)), first calculate f(-3) which is 27, then use this result to find f(27), resulting in the value 2187.

Step-by-step explanation:

The student is asking to determine the value of the composition of the function f(f(-3)). To solve this, we'll first need to calculate the value of f(-3) and then use this result as the input for the function f again.

First, let's find f(-3):

• f(-3) = 3(-3)2 = 3(9) = 27

Now, we'll use the result from f(-3), which is 27, as our new input value for f:

• f(27) = 3(27)2 = 3(729) = 2187

So, the value of the composition f(f(-3)) is 2187.