Question

Let f(x) = x^2 + 2x and g(x) = 2x. Evaluate the composition (fºg)(2).

Answer 1

B. (f o g)(2) = 24

General Formulas and Concepts;

Pre-Algebra

• Order of Operations: BPEMDAS

Algebra I

• Composition of functions

Explanation:

Step 1: Define

f(x) = x² + 2x

g(x) = 2x

Step 2: Find (f o g)(x)

1. Substitute: (f o g)(x) = (2x)² + 2(2x)
2. Evaluate: (f o g)(x) = 4x² + 2(2x)
3. Multiply: (f o g)(x) = 4x² + 4x

Step 3: Find (f o g)(2)

1. Substitute: (f o g)(2) = 4(2)² + 4(2)
2. Evaluate: (f o g)(2) = 4(4) + 4(2)
3. Multiply: (f o g)(2) = 16 + 8
4. Add: (f o g)(2) = 24

And we have our final answer!

Answer 2

B

Explanation:

We have the two functions:

`f(x)=x^2+2x\text{ and } g(x)=2x`

And we want to evaluate:

`(f\circ g)(2)`

This is equivalent to:

`=f(g(2))`

Hence, we will evaluate g(2) first.

Therefore:

`g(2)=2(2)=4`

We can now substitute this for f(g(2)). Hence:

`f(g(2))=f(4)`

Evaluate:

`f(4)=(4)^2+2(4)=16+8=24`

Therefore:

`(f\circ g)(2)=24`

Hence, our answer is B.