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

To find \( f(g(1)) \), we first need to evaluate \( g(1) \) and then use this result as the input for \( f(x) \).

Given the functions:

\[
f(x) = x^3 + 5x
\]
\[
g(x) = 2x + 1
\]

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

2. **Substitute \( g(1) \) into \( f(x) \) to find \( f(g(1)) \):**
   \[
   f(g(1)) = f(3)
   \]
   Now, calculate \( f(3) \):
   \[
   f(3) = 3^3 + 5(3) = 27 + 15 = 42
   \]

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

Would you like more details or have any questions?

Here are 5 related questions:
1. What is \( f(g(x)) \) in general terms?
2. How do you find the derivative of \( f(x) \) or \( g(x) \)?
3. Can you determine the inverse function of \( f(x) \) or \( g(x) \)?
4. What would be the value of \( f(g(-1)) \)?
5. How does the composition of functions change if \( g(x) \) was a quadratic function?

**Tip:** When working with compositions of functions, always start by evaluating the innermost function.

Explore how to solve the function composition f(g(x)) problem with detailed steps and examples. This problem involves evaluating polynomial functions and understanding the composition of functions. Suitable for Grades 10-12 students.

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