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The function given is \( f(x) = 3x^2 + 5 \), and you are asked to find \( f(3x) \).

To do this, substitute \( 3x \) in place of \( x \) in the function \( f(x) \).

\[
f(3x) = 3(3x)^2 + 5
\]

Now, calculate the square of \( 3x \):

\[
(3x)^2 = 9x^2
\]

Thus, the equation becomes:

\[
f(3x) = 3(9x^2) + 5 = 27x^2 + 5
\]

So, the answer is:

\[
f(3x) = 27x^2 + 5
\]

Let me know if you'd like any further clarification or more details.

Here are some related questions you could explore:
1. What is \( f(2x) \) for the same function \( f(x) = 3x^2 + 5 \)?
2. How would you find \( f(x + 1) \) instead of \( f(3x) \)?
3. What is the derivative of \( f(x) = 3x^2 + 5 \)?
4. What happens to the graph of \( f(x) \) when you evaluate \( f(3x) \)?
5. What is the inverse function of \( f(x) = 3x^2 + 5 \), if possible?

**Tip:** When substituting an expression into a function, always remember to apply the operation to the entire expression, not just the variable.

The function f is defined by f(x) = 3x^2 + 5. Find f(3x).

This problem involves finding f(3x) for the function f(x) = 3x^2 + 5 using substitution. It requires an understanding of quadratic functions and substitution rules. Suitable for students in Grades 9-10.

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