Question

Suppose a function f is defined recursively as f(n+1)=(f(n))²+ f(n)+1, f(0)=1. Use this definition to calculate

f(1)

Answer 1

To calculate f(1) for the given recursive function definition, f(0) is plugged into the formula, resulting in f(1) being equal to 3.

Step-by-step explanation:

The student is asking how to calculate f(1) given a recursive definition of a function where f(n+1)=(f(n))²+ f(n)+1 and f(0)=1. To find f(1), we will use the base value f(0) and plug it into the given recursive formula.

Using the definition:

• f(1) = (f(0))² + f(0) + 1
• f(1) = (1)² + 1 + 1
• f(1) = 1 + 1 + 1
• f(1) = 3

Therefore, the value of f(1) is 3.