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

Given function and initial condition: We are given the recursive function f(n) = f(n-1)^(2) - n, and the initial condition f(1) = 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 initial condition f(1) = 1. f(2) = f(2-1)^(2) - 2 f(2) = f(1)^(2) - 2 f(2) = 1^(2) - 2 f(2) = 1 - 2 f(2) = -1Find f(3): Next, we find f(3) using the value of f(2) we just found. f(3) = f(3-1)^(2) - 3 f(3) = f(2)^(2) - 3 f(3) = (-1)^(2) - 3 f(3) = 1 - 3 f(3) = -2Find f(4): Finally, we find f(4) using the value of f(3). f(4) = f(4-1)^(2) - 4 f(4) = f(3)^(2) - 4 f(4) = (-2)^(2) - 4 f(4) = 4 - 4 f(4) = 0

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

If $f(1)=1$ and $f(n)=f(n-1)^{2}-n$ 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)=1

and

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

then find the value of

f(4)

\newline

Answer:

Given function and initial condition: We are given the recursive function $f(n) = f(n-1)^{2} - n$ , and the initial condition $f(1) = 1$ . 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 initial condition $f(1) = 1$ .
$f(2) = f(2-1)^{2} - 2$
$f(2) = f(1)^{2} - 2$
$f(2) = 1^{2} - 2$
$f(2) = 1 - 2$
$f(2) = -1$
Find $f(3)$ : Next, we find $f(3)$ using the value of $f(2)$ we just found. $\newline$ $f(3) = f(3-1)^{2} - 3$ $\newline$ $f(3) = f(2)^{2} - 3$ $\newline$ $f(3) = (-1)^{2} - 3$ $\newline$ $f(3) = 1 - 3$ $\newline$ $f(3) = -2$
Find $f(4)$ : Finally, we find $f(4)$ using the value of $f(3)$ .
$f(4) = f(4-1)^{2} - 4$
$f(4) = f(3)^{2} - 4$
$f(4) = (-2)^{2} - 4$
$f(4) = 4 - 4$
$f(4) = 0$