If f(x)=x³+5x and g(x)=2x+1,then find fg(1)

Given the functions \( f(x) = x^3 + 5x \) and \( g(x) = 2x + 1 \), you want to find \( f(g(1)) \).

Here's how to solve it step by step:

1. **Evaluate \( g(1) \):**
   \[
   g(1) = 2(1) + 1 = 2 + 1 = 3
   \]

2. **Substitute \( g(1) \) into \( f(x) \):**
   \[
   f(g(1)) = f(3)
   \]

3. **Evaluate \( f(3) \):**
   \[
   f(3) = 3^3 + 5(3) = 27 + 15 = 42
   \]

So, \( f(g(1)) = 42 \).

Would you like more details or have any questions?

Here are five related questions you might find interesting:
1. How would you find \( g(f(1)) \) with the same functions?
2. What happens if you compose these functions in reverse order?
3. How do you differentiate \( f(g(x)) \) using the chain rule?
4. Can you graph \( f(x) \) and \( g(x) \) to visualize the composition?
5. What is the significance of the composition of functions in real-world applications?

**Tip:** When composing functions, always remember to evaluate the innermost function first before applying the outer function.

Understand how to evaluate the composition of functions f(x) = x^3 + 5x and g(x) = 2x + 1. Step-by-step solution to find f(g(1)), involving function substitution and calculation. Suitable for Grades 10-12.

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