If f(1)=1 and f(n)=f(n-1)^(2)-4 then find the value of f(3). Answer:

Find f(2): We are given the initial condition f(1) = 1 and the recursive formula f(n) = f(n-1)^(2) - 4. To find f(3), we first need to find f(2). Using the recursive formula, we substitute n = 2 to find f(2): f(2) = f(2-1)^(2) - 4 f(2) = f(1)^(2) - 4 f(2) = 1^(2) - 4 f(2) = 1 - 4 f(2) = -3Calculate f(3): Now that we have f(2) = -3, we can use this value to find f(3). Using the recursive formula again, we substitute n = 3 to find f(3): f(3) = f(3-1)^(2) - 4 f(3) = f(2)^(2) - 4 f(3) = (-3)^(2) - 4 f(3) = 9 - 4 f(3) = 5

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If
f(1)=1 and
f(n)=f(n-1)^(2)-4 then find the value of
f(3).
Answer:

If $f(1)=1$ and $f(n)=f(n-1)^{2}-4$ then find the value of $f(3)$ . $\newline$ Answer:

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Math Problems

Algebra 2

Evaluate expression when two complex numbers are given

Full solution

Q. If

f(1)=1

and

f(n)=f(n-1)^{2}-4

then find the value of

f(3)

\newline

Answer:

Find $f(2)$ : We are given the initial condition $f(1) = 1$ and the recursive formula $f(n) = f(n-1)^{2} - 4$ . To find $f(3)$ , we first need to find $f(2)$ . Using the recursive formula, we substitute $n = 2$ to find $f(2)$ : $f(2) = f(2-1)^{2} - 4$ $f(2) = f(1)^{2} - 4$ $f(2) = 1^{2} - 4$ $f(1) = 1$ $0$ $f(1) = 1$ $1$
Calculate $f(3)$ : Now that we have $f(2) = -3$ , we can use this value to find $f(3)$ . Using the recursive formula again, we substitute $n = 3$ to find $f(3)$ : $f(3) = f(3-1)^{2} - 4$ $f(3) = f(2)^{2} - 4$ $f(3) = (-3)^{2} - 4$ $f(3) = 9 - 4$ $f(3) = 5$