SAT Math Practice Question #21610 - SATify | SATify

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SAT Math Practice Question #21610 - SATify | SATify

#21610

algebra

functions

Recurrence Relations

hard

120 sec

Let $f$ be a function with the following properties:
(i) $f (1) = 1$ , and
(ii) $f (2 n) = \frac{1}{n} f (n)$ for any positive integer $n$ .
What is the value of $f (2^{10})$ ?

A.

$2^{45}$

B.

$2^{- 45}$

C.

$2^{- 55}$

D.

$2^{55}$

E.

$2^{10}$