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

Initial Condition Calculation: We are given the initial condition f(1) = 2. We need to use the recursive formula f(n+1) = f(n)^(2) - 3 to find f(2). Calculation: f(2) = f(1)^(2) - 3 = 2^2 - 3 = 4 - 3 = 1.Finding f(3): Now that we have f(2), we can find f(3) using the same recursive formula. Calculation: f(3) = f(2)^(2) - 3 = 1^2 - 3 = 1 - 3 = -2.Finding f(4): Finally, we use f(3) to find f(4). Calculation: f(4) = f(3)^(2) - 3 = (-2)^2 - 3 = 4 - 3 = 1.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

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

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

View step-by-step help

Home

Math Problems

Precalculus

Find the roots of factored polynomials

Full solution

Q. If

f(1)=2

and

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

then find the value of

f(4)

\newline

Answer:

Initial Condition Calculation: We are given the initial condition $f(1) = 2$ . We need to use the recursive formula $f(n+1) = f(n)^{2} - 3$ to find $f(2)$ . $\newline$ Calculation: $f(2) = f(1)^{2} - 3 = 2^2 - 3 = 4 - 3 = 1$ .
Finding $f(3)$ : Now that we have $f(2)$ , we can find $f(3)$ using the same recursive formula. $\newline$ Calculation: $f(3) = f(2)^{2} - 3 = 1^{2} - 3 = 1 - 3 = -2$ .
Finding $f(4)$ : Finally, we use $f(3)$ to find $f(4)$ . $\newline$ Calculation: $f(4) = f(3)^{2} - 3 = (-2)^{2} - 3 = 4 - 3 = 1$ .