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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].
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