Let's go through the problem step-by-step.
### Step 1: Define the Function f(x)
Given the function:
[tex]\[ f(x) = x^2 \][/tex]
### Step 2: Calculate [tex]\( f(x) + f(x) + f(x) \)[/tex]
First, we need to evaluate [tex]\( f(x) \)[/tex]:
[tex]\[ f(x) = x^2 \][/tex]
Adding this function three times:
[tex]\[ f(x) + f(x) + f(x) \][/tex]
[tex]\[ = x^2 + x^2 + x^2 \][/tex]
[tex]\[ = 3x^2 \][/tex]
So,
[tex]\[ f(x) + f(x) + f(x) = 3x^2 \][/tex]
### Step 3: Calculate [tex]\( 3 f(x) \)[/tex]
Next, we calculate [tex]\( 3 f(x) \)[/tex]:
[tex]\[ 3 f(x) \][/tex]
[tex]\[ = 3 \cdot (x^2) \][/tex]
[tex]\[ = 3x^2 \][/tex]
So,
[tex]\[ 3 f(x) = 3x^2 \][/tex]
### Step 4: Evaluate [tex]\( 3 f(2) \)[/tex]
Finally, we evaluate [tex]\( 3 f(2) \)[/tex]:
[tex]\[ f(x) = x^2 \][/tex]
[tex]\[ f(2) = 2^2 = 4 \][/tex]
Thus,
[tex]\[ 3 f(2) = 3 \cdot f(2) \][/tex]
[tex]\[ = 3 \cdot 4 \][/tex]
[tex]\[ = 12 \][/tex]
### Summary
- [tex]\( f(x) + f(x) + f(x) = 3x^2 \)[/tex]
- [tex]\( 3 f(x) = 3x^2 \)[/tex]
- [tex]\( 3 f(2) = 12 \)[/tex]
