Answer:

Step-by-step explanation:
We are provided with the following functions:
f(x) = x² + 2x + 3

The given problem also requires to find the Composition of Functions, f(g(x)) when x = 2.
The <u>Composition of Function</u> <em>f</em> with function <em>g</em> can be expressed as ( <em>f ° g </em>)(x) = f(g(x)). In solving for the composition of functions, we must first evaluate the <em>innermost</em> function, g(x), then use the output as an input for f(x).
<h2>Solve for f(g(x)) when x = 2:</h2><h3><u>Find g(x):</u></h3>
Starting with g(x), we will use x = 2 as an <u>input</u> value into the function:


Transform the first term, x = 2, into a fraction with a denominator of 3 to combine with 4/3:




<h3><u>Find f(x):</u></h3>
Next, we will use
as input for the function, f(x) = x² + 2x + 3:
f(x) = x² + 2x + 3

Use the <u>Quotient-to-Power Rule of Exponents</u> onto the <em>leading term </em>(x²):

Multiply the numerator (10) of the middle term by 2:

- Determine the <u>least common multiple (LCM)</u> of the denominators from the previous step: 9, 3, and 1 (which is 9).
- Then, transform the denominators of 20/3 and 3/1 on the <u>right-hand side</u> of the equation into like-fractions:


Finally, add the three fractions on the right-hand side of the equation:

<h2>Final Answer:</h2>

<h3>______________________________</h3>
<em>Keywords:</em>
Composition of functions
f o g
f (g(x))
____________________________________
Learn more about <u><em>Composition of Functions</em></u> here:
brainly.com/question/11388036