Let's work through the problem step by step to find the correct simplified form of [tex]\( f(x) + f(x) + f(x) \)[/tex].
1. Understanding the Expression:
The expression given is [tex]\( f(x) + f(x) + f(x) \)[/tex]. To simplify, we combine the terms of [tex]\( f(x) \)[/tex].
2. Combining the Terms:
When we add [tex]\( f(x) \)[/tex] three times, we get:
[tex]\[
f(x) + f(x) + f(x) = 3 \cdot f(x)
\][/tex]
3. Simplified Form:
The simplified form of the expression [tex]\( f(x) + f(x) + f(x) \)[/tex] is therefore:
[tex]\[
3 f(x)
\][/tex]
4. Comparing with Choices:
We are given a set of choices to match with our simplified form [tex]\( 3 f(x) \)[/tex]:
[tex]\[
\begin{array}{l}
\text{DONG} \\
3x \\
3x^2 \\
x^2+3
\end{array}
\][/tex]
Here, the value [tex]\( 3 f(x) \)[/tex] directly corresponds to the general form [tex]\( 3 f(x) \)[/tex], but if we're translating [tex]\( f(x) \)[/tex] itself into a common function like [tex]\( x \)[/tex] or [tex]\( x^2 \)[/tex], we must ensure the expressions match.
Based on the choices, the appropriate match would be:
[tex]\[
3x
\][/tex]
Thus, the correct choice from the given options is:
3x
