Answered

At Westonci.ca, we connect you with experts who provide detailed answers to your most pressing questions. Start exploring now! Discover detailed solutions to your questions from a wide network of experts on our comprehensive Q&A platform. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.

If [tex]f(x) = x^2 + 3x + 5[/tex], what is [tex]f(3+h)[/tex]?

A. [tex]h^2 + h + 23[/tex]
B. [tex](3+h)^2 + 8 + h[/tex]
C. [tex]h^2 + 9h + 23[/tex]
D. [tex]\left(x^2 + 3x + 5\right)(3+h)[/tex]

Sagot :

GinnyAnswer
Sure, let's find [tex]\( f(3+h) \)[/tex] if [tex]\( f(x) = x^2 + 3x + 5 \)[/tex].

### Step-by-step Solution:

1. Substitute [tex]\( 3 + h \)[/tex] for [tex]\( x \)[/tex] in the function [tex]\( f(x) \)[/tex]:
[tex]\[ f(3+h) = (3+h)^2 + 3(3+h) + 5 \][/tex]

2. Expand the terms:
[tex]\[ (3+h)^2 = 9 + 6h + h^2 \][/tex]
[tex]\[ 3(3+h) = 9 + 3h \][/tex]

3. Combine all the terms:
[tex]\[ f(3+h) = (9 + 6h + h^2) + (9 + 3h) + 5 \][/tex]

4. Simplify by combining like terms:
[tex]\[ f(3+h) = h^2 + 6h + 3h + 9 + 9 + 5 \][/tex]
[tex]\[ f(3+h) = h^2 + 9h + 23 \][/tex]

Therefore, the correct answer is:

C. [tex]\( h^2 + 9h + 23 \)[/tex]

So, [tex]\( f(3 + h) = h^2 + 9h + 23 \)[/tex].
We hope this was helpful. Please come back whenever you need more information or answers to your queries. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.