If f(1)=1 and f(n)=f(n-1)^(2)-n then find the value of f(3). Answer:

Given Recursive Function: We are given the recursive function f(n) = f(n-1)^(2) - n and the initial condition f(1) = 1. To find f(3), we first need to find f(2).Find f(2): Using the recursive formula, we substitute n = 2 to find f(2). f(2) = f(2-1)^(2) - 2 f(2) = f(1)^(2) - 2 Since we know f(1) = 1, we can substitute that in. f(2) = 1^(2) - 2 f(2) = 1 - 2 f(2) = -1Find f(3): Now that we have f(2), we can use it to find f(3). f(3) = f(3-1)^(2) - 3 f(3) = f(2)^(2) - 3 Substitute the value of f(2) we found in the previous step. f(3) = (-1)^(2) - 3 f(3) = 1 - 3 f(3) = -2

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

If
f(1)=1 and
f(n)=f(n-1)^(2)-n then find the value of
f(3).
Answer:

If $f(1)=1$ and $f(n)=f(n-1)^{2}-n$ then find the value of $f(3)$ . $\newline$ Answer:

View step-by-step help

Home

Math Problems

Algebra 2

Evaluate expression when two complex numbers are given

Full solution

Q. If

f(1)=1

and

f(n)=f(n-1)^{2}-n

then find the value of

f(3)

\newline

Answer:

Given Recursive Function: We are given the recursive function $f(n) = f(n-1)^{2} - n$ and the initial condition $f(1) = 1$ . To find $f(3)$ , we first need to find $f(2)$ .
Find $f(2)$ : Using the recursive formula, we substitute $n = 2$ to find $f(2)$ .
$f(2) = f(2-1)^{2} - 2$
$f(2) = f(1)^{2} - 2$
Since we know $f(1) = 1$ , we can substitute that in.
$f(2) = 1^{2} - 2$
$f(2) = 1 - 2$
$f(2) = -1$
Find $f(3)$ : Now that we have $f(2)$ , we can use it to find $f(3)$ .
$f(3) = f(3-1)^{2} - 3$
$f(3) = f(2)^{2} - 3$
Substitute the value of $f(2)$ we found in the previous step.
$f(3) = (-1)^{2} - 3$
$f(3) = 1 - 3$
$f(3) = -2$