To address the problems given, we will use the function [tex]\( f(x) = x^2 \)[/tex].
1. Finding [tex]\( f(x) + f(x) + f(x) \)[/tex]
First, we need to add the function [tex]\( f(x) \)[/tex] three times:
[tex]\[
f(x) + f(x) + f(x)
\][/tex]
Since each [tex]\( f(x) \)[/tex] is [tex]\( x^2 \)[/tex]:
[tex]\[
f(x) + f(x) + f(x) = x^2 + x^2 + x^2 = 3x^2
\][/tex]
So:
[tex]\[
f(x) + f(x) + f(x) = 3f(x)
\][/tex]
[tex]\[
3f(x) = 3x^2
\][/tex]
2. Evaluate [tex]\( 3f(2) \)[/tex]
To evaluate [tex]\( 3f(2) \)[/tex], we first need to find [tex]\( f(2) \)[/tex]:
[tex]\[
f(2) = 2^2 = 4
\][/tex]
Then we calculate:
[tex]\[
3 f(2) = 3 \times 4 = 12
\][/tex]
Thus, summarizing the steps and results:
1. [tex]\( f(x) + f(x) + f(x) = 3f(x) \)[/tex]
2. [tex]\( 3f(x) = 3x^2 \)[/tex]
3. [tex]\( 3f(2) = 12 \)[/tex]
Therefore, the evaluated answers are:
1. [tex]\( f(x) + f(x) + f(x) = 3f(x) \)[/tex]
2. [tex]\( 3f(x) = 3x^2 \)[/tex]
3. [tex]\( 3f(2) = 12 \)[/tex]
