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

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

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Evaluate expression when two complex numbers are given

Full solution

Q. If

f(1)=2

and

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

then find the value of

f(4)

.

\newline

Answer:

Given conditions: We are given the initial condition and the recursive formula: $\newline$ $f(1) = 2$ $\newline$ $f(n+1) = f(n)^{2} - 1$ $\newline$ We need to find $f(4)$ . To do this, we will calculate $f(2)$ , $f(3)$ , and then $f(4)$ using the recursive formula.
Find $f(2)$ : First, we find $f(2)$ using the given formula with $n=1$ :
$f(2) = f(1)^{2} - 1$
Substitute $f(1) = 2$ into the formula:
$f(2) = (2)^{2} - 1$
$f(2) = 4 - 1$
$f(2) = 3$
Find $f(3)$ : Next, we find $f(3)$ using the given formula with $n=2$ :
$f(3) = f(2)^{2} - 1$
Substitute $f(2) = 3$ into the formula:
$f(3) = (3)^{2} - 1$
$f(3) = 9 - 1$
$f(3) = 8$
Find $f(4)$ : Finally, we find $f(4)$ using the given formula with $n=3$ : $f(4) = f(3)^{2} - 1$ Substitute $f(3) = 8$ into the formula: $f(4) = (8)^{2} - 1$ $f(4) = 64 - 1$ $f(4) = 63$

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