Answered

Discover the answers to your questions at Westonci.ca, where experts share their knowledge and insights with you. Our platform offers a seamless experience for finding reliable answers from a network of experienced professionals. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.

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].
Thanks for using our platform. We're always here to provide accurate and up-to-date answers to all your queries. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.