Sure, let's solve each part of the question step-by-step.
### Step 1: Calculate [tex]\( f(x) + f(x) + f(x) \)[/tex]
Given the function:
[tex]\[ f(x) = x^2 \][/tex]
First, calculate [tex]\( f(x) \)[/tex]:
[tex]\[ f(x) = x^2 \][/tex]
Next, sum [tex]\( f(x) \)[/tex] three times:
[tex]\[ f(x) + f(x) + f(x) = x^2 + x^2 + x^2 \][/tex]
Combine the terms:
[tex]\[ x^2 + x^2 + x^2 = 3x^2 \][/tex]
So:
[tex]\[ f(x) + f(x) + f(x) = 3x^2 \][/tex]
### Step 2: Calculate [tex]\( 3 f(x) \)[/tex]
We already know that:
[tex]\[ f(x) = x^2 \][/tex]
Now multiply [tex]\( f(x) \)[/tex] by 3:
[tex]\[ 3 f(x) = 3 \cdot x^2 \][/tex]
So:
[tex]\[ 3 f(x) = 3x^2 \][/tex]
### Step 3: Evaluate [tex]\( 3 f(2) \)[/tex]
First, substitute [tex]\( x = 2 \)[/tex] into the function [tex]\( f(x) \)[/tex]:
[tex]\[ f(2) = 2^2 = 4 \][/tex]
Next, calculate [tex]\( 3 f(2) \)[/tex]:
[tex]\[ 3 f(2) = 3 \cdot 4 = 12 \][/tex]
### Summary of the answers
1. [tex]\( f(x) + f(x) + f(x) = 3x^2 \)[/tex]
2. [tex]\( 3 f(x) = 3x^2 \)[/tex]
3. [tex]\( 3 f(2) = 12 \)[/tex]
These are the final solutions to each part of the question.
