If f(1)=4 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) = 4 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 given formula and the initial condition f(1) = 4. f(2) = f(1)^(2) - 1 f(2) = 4^2 - 1 f(2) = 16 - 1 f(2) = 15Find f(3): Next, we find f(3) using the value of f(2) we just calculated. f(3) = f(2)^(2) - 1 f(3) = 15^2 - 1 f(3) = 225 - 1 f(3) = 224Find f(4): Finally, we find f(4) using the value of f(3). f(4) = f(3)^(2) - 1 f(4) = 224^2 - 1 f(4) = 50176 - 1 f(4) = 50175

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

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

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Algebra 2

Evaluate expression when two complex numbers are given

Full solution

Q. If

f(1)=4

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 $f(1) = 4$ 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 given formula and the initial condition $f(1) = 4$ .
$f(2) = f(1)^{2} - 1$
$f(2) = 4^2 - 1$
$f(2) = 16 - 1$
$f(2) = 15$
Find $f(3)$ : Next, we find $f(3)$ using the value of $f(2)$ we just calculated. $\newline$ $f(3) = f(2)^{2} - 1$ $\newline$ $f(3) = 15^{2} - 1$ $\newline$ $f(3) = 225 - 1$ $\newline$ $f(3) = 224$
Find $f(4)$ : Finally, we find $f(4)$ using the value of $f(3)$ .
$f(4) = f(3)^{2} - 1$
$f(4) = 224^{2} - 1$
$f(4) = 50176 - 1$
$f(4) = 50175$