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

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

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Evaluate expression when a complex numbers and a variable term is given

Full solution

Q. If

f(1)=1

and

f(n)=f(n-1)^{2}+3

then find the value of

f(3)

.

\newline

Answer:

Find $f(2)$ : Given the recursive function $f(n) = f(n-1)^{2} + 3$ and the initial condition $f(1) = 1$ , we need to find $f(3)$ . We will start by finding $f(2)$ .
$f(2) = f(2-1)^{2} + 3$
$f(2) = f(1)^{2} + 3$
Since we know $f(1) = 1$ , we substitute this value into the equation.
$f(2) = (1)^{2} + 3$
$f(2) = 1 + 3$
$f(n) = f(n-1)^{2} + 3$ $0$
Find $f(3)$ : Now that we have $f(2)$ , we can find $f(3)$ using the same recursive formula. $\newline$ $f(3) = f(3-1)^{2} + 3$ $\newline$ $f(3) = f(2)^{2} + 3$ $\newline$ We already found that $f(2) = 4$ , so we substitute this value into the equation. $\newline$ $f(3) = (4)^{2} + 3$ $\newline$ $f(3) = 16 + 3$ $\newline$ $f(3) = 19$

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