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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:

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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.
$f(3) = (-1)^{2} - 3$
$f(3) = 1 - 3$
$f(3) = -2$

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