Respuesta :

xKelvin

Answer:

B

Step-by-step explanation:

We have the two functions:

[tex]f(x)=x^2+2x\text{ and } g(x)=2x[/tex]

And we want to evaluate:

[tex](f\circ g)(2)[/tex]

This is equivalent to:

[tex]=f(g(2))[/tex]

Hence, we will evaluate g(2) first.

Therefore:

[tex]g(2)=2(2)=4[/tex]

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

[tex]f(g(2))=f(4)[/tex]

Evaluate:

[tex]f(4)=(4)^2+2(4)=16+8=24[/tex]

Therefore:

[tex](f\circ g)(2)=24[/tex]

Hence, our answer is B.

Space

Answer:

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

General Formulas and Concepts;

Pre-Algebra

  • Order of Operations: BPEMDAS

Algebra I

  • Composition of functions

Step-by-step 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!