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

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

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Evaluate exponential functions

Full solution

Q. If

f(1)=1

and

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

then find the value of

f(3)

.

\newline

Answer:

Given $f(1)=1$ : We are given that $f(1)=1$ . To find $f(3)$ , we first need to find $f(2)$ using the recursive formula $f(n+1)=f(n)^{2}+2$ . $\newline$ Calculate $f(2)$ using $f(1)$ : $\newline$ $f(2) = f(1)^{2} + 2$ $\newline$ $f(2) = 1^{2} + 2$ $\newline$ $f(2) = 1 + 2$ $\newline$ $f(1)=1$ $0$
Calculate $f(2)$ : Now that we have $f(2)=3$ , we can use this value to find $f(3)$ using the same recursive formula. $\newline$ Calculate $f(3)$ using $f(2)$ : $\newline$ $f(3) = f(2)^{2} + 2$ $\newline$ $f(3) = 3^{2} + 2$ $\newline$ $f(3) = 9 + 2$ $\newline$ $f(3) = 11$

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