What is the value of f(g(4)) if f(x) = 3x² and g(x) = 2x + 5?

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To find the value of f(g(4)), we need to break this problem down into two steps: first, we need to evaluate g(4), and second, we will use that result to evaluate f.

Step 1: Calculate g(4)

Given the function g(x) = 2x + 5, we substitute 4 for x:

g(4) = 2(4) + 5
    = 8 + 5
    = 13

So, we find that g(4) = 13.

Step 2: Calculate f(g(4)) or f(13)

Now that we have g(4), we can evaluate f(13) using the function f(x) = 3x²:

f(13) = 3(13)²
      = 3(169)
      = 507

Thus, the value of f(g(4)) or f(13) is 507.

Final Result

The calculated value of f(g(4)) is 507.

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