Solve for addition in functions   g (a) =a³+5a² f(a) =2a+4 find g(3)+f(3)

To solve \( g(3) + f(3) \), we need to first find \( g(3) \) and \( f(3) \) using the given functions.

1. **Given functions:**
   \[
   g(a) = a^3 + 5a^2
   \]
   \[
   f(a) = 2a + 4
   \]

2. **Calculate \( g(3) \):**
   \[
   g(3) = 3^3 + 5(3)^2
   \]
   \[
   g(3) = 27 + 5(9)
   \]
   \[
   g(3) = 27 + 45 = 72
   \]

3. **Calculate \( f(3) \):**
   \[
   f(3) = 2(3) + 4
   \]
   \[
   f(3) = 6 + 4 = 10
   \]

4. **Now, find \( g(3) + f(3) \):**
   \[
   g(3) + f(3) = 72 + 10 = 82
   \]

So, \( g(3) + f(3) = 82 \).

Would you like more details or have any questions?

Here are 5 related questions:
1. What is the derivative of the function \( g(a) = a^3 + 5a^2 \)?
2. How do you find the roots of the function \( f(a) = 2a + 4 \)?
3. What would \( g(4) + f(4) \) be?
4. How can we determine the maximum or minimum value of the function \( g(a) \)?
5. What are the possible values of \( a \) where \( g(a) = f(a) \)?

**Tip:** When dealing with functions, always substitute the value of the variable correctly to avoid calculation mistakes.

Learn how to calculate g(3) + f(3) using the functions g(a) = a³ + 5a² and f(a) = 2a + 4 with step-by-step solutions. This problem covers polynomial evaluation, basic arithmetic operations, and function evaluation. Suitable for students in Grades 7-9.

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