If f(1)=3 and f(n)=f(n-1)^(2)-1 then find the value of f(4). Answer:

Given Initial Condition: We are given the initial condition f(1) = 3 and the recursive formula f(n) = f(n-1)^(2) - 1. To find f(4), we need to find the values of f(2), f(3), and then f(4) using the recursive formula.Find f(2): First, let's find f(2) using the recursive formula and the initial condition. f(2) = f(1)^(2) - 1 = 3^2 - 1 = 9 - 1 = 8 So, f(2) = 8.Find f(3): Next, we find f(3) using the value of f(2). f(3) = f(2)^(2) - 1 = 8^2 - 1 = 64 - 1 = 63 So, f(3) = 63.Find f(4): Finally, we find f(4) using the value of f(3). f(4) = f(3)^(2) - 1 = 63^2 - 1 = 3969 - 1 = 3968 So, f(4) = 3968.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

If
f(1)=3 and
f(n)=f(n-1)^(2)-1 then find the value of
f(4).
Answer:

If $f(1)=3$ and $f(n)=f(n-1)^{2}-1$ then find the value of $f(4)$ . $\newline$ 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)=3

and

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

then find the value of

f(4)

\newline

Answer:

Given Initial Condition: We are given the initial condition $f(1) = 3$ and the recursive formula $f(n) = f(n-1)^{2} - 1$ . To find $f(4)$ , we need to find the values of $f(2)$ , $f(3)$ , and then $f(4)$ using the recursive formula.
Find $f(2)$ : First, let's find $f(2)$ using the recursive formula and the initial condition. $f(2) = f(1)^{2} - 1$ $= 3^{2} - 1$ $= 9 - 1$ $= 8$ So, $f(2) = 8$ .
Find $f(3)$ : Next, we find $f(3)$ using the value of $f(2)$ .
$f(3) = f(2)^{2} - 1$
= $8^{2} - 1$
= $64 - 1$
= $63$
So, $f(3) = 63$ .
Find $f(4)$ : Finally, we find $f(4)$ using the value of $f(3)$ .
$f(4) = f(3)^{2} - 1$
= $63^{2} - 1$
= $3969 - 1$
= $3968$
So, $f(4) = 3968$ .