given f(x)=2x-15, g(x)=x²+19x and h(x)=√x+6, find f(f(f(f(15)

To solve the expression \( f(f(f(f(15)))) \) where \( f(x) = 2x - 15 \), we can follow these steps:

### Step 1: Calculate \( f(15) \)
\[ f(15) = 2(15) - 15 \]
\[ f(15) = 30 - 15 \]
\[ f(15) = 15 \]

### Step 2: Calculate \( f(f(15)) \)
Since \( f(15) = 15 \), we need to find \( f(15) \) again:
\[ f(f(15)) = f(15) = 15 \]

### Step 3: Calculate \( f(f(f(15))) \)
Now, calculate \( f(f(f(15))) \):
\[ f(f(f(15))) = f(15) = 15 \]

### Step 4: Calculate \( f(f(f(f(15)))) \)
Finally, calculate \( f(f(f(f(15)))) \):
\[ f(f(f(f(15)))) = f(15) = 15 \]

### Final Answer:
\[ f(f(f(f(15)))) = 15 \]

This sequence leads to the final answer being \( 15 \).

Would you like any further details, or do you have any questions?

### Related Questions:
1. How would the calculation change if the initial value was different?
2. What if \( f(x) = 3x - 20 \), how would the answer change?
3. What happens when a function iterates a different number of times, say 3 or 5?
4. Can you explain the concept of fixed points in a function?
5. How would \( f(f(f(f(20)))) \) differ in this scenario?
6. Can you explore the behavior of the function \( g(x) = x^2 + 19x \) under similar iterations?
7. What would happen if we included \( h(x) = \sqrt{x} + 6 \) in this iteration?
8. How does the iterative process change when non-linear functions are involved?

### Tip:
When working with iterative functions, recognizing fixed points (where \( f(x) = x \)) can simplify calculations significantly.

Explore how to calculate f(f(f(f(15)))) using iterative functions with a step-by-step solution. Understand the concept of function iteration and fixed points in mathematical functions.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation