Question

A sequence is defined by the recursive function f(n 1) = one-halff(n). if f(3) = 9 , what is f(1) ?

Answer 1

$f(1)$ is $81.$

What is a recursive function?

• A recursive function generates a series of phrases by repeating or using its own prior term as input.
• Problems that can be split down into smaller, repeating problems are ideal for recursion to solve. It is particularly useful when working on issues with numerous potential solutions that are too complex to handle iteratively. Searching a file system is an effective illustration of this.
• A recursive formula is one that defines each term in a sequence by reference to the one before it.

To find  f(1):

f(n 1) = one-half(n).

f(3) = 9.

$f(3) = 9If n = 1,f(2) = 9×3f(2) = 27If n = 0,f(1) = 27 ×3f(1) = 81$

A sequence is defined by the recursive function $f(1)$ is $81.$

To learn more about recursive functions, refer to:

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Answer 2

Answer:

36

Step-by-step explanation:

Assuming I understand the question correctly

$\text{one-halff(n)} = \frac{1}{2} f(n)$

We have the recursive relationship

$f(n+1) = \frac{1}{2} f(n)$

$f(3) = 9$

$f(3) = \frac{1}{2} f(2)$

$f(2) = \frac{1}{2} f(1)$

So

$f(3) = \frac{1}{2} (\frac{1}{2} f(1) = \frac{1}{4} f(1)$

So $f(1) = 4f(3) = 4(9) = 36$

Verifying

If f(1) = 36 then f(2) = (1/2)f(1) = (1/2)36 = 18

f(3) = (1/2) f(2) = (1/2)(18) = 9