For all integers x>0, let f(x) be defined as f(x)=f(x−1)/(−1)^x. If f(1)=1, which of the following statement is correct for the values of f(x)? A) The values of f(x) for all even values of x is the same. B) The value of f(x) for all odd values of x is the same. C) The value of f(x) for all even values is 1 and for all odd values is -1 D) The value of f(x) is either 1 or -1

Define Function: Define the function based on the given recursive formula and initial condition. Calculate f(2) using f(1). f(2) = f(1) / (-1)^2 = 1 / 1 = 1. Calculate f(2): Calculate f(3) using f(2). f(3) = f(2) / (-1)^3 = 1 / -1 = -1. Calculate f(3): Calculate f(4) using f(3). f(4) = f(3) / (-1)^4 = -1 / 1 = -1.

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For all integers x>0, let $f(x)$ be defined as $f(x)=\frac{f(x-1)}{(-1)^x}$ . If $f(1)=1$ , which of the following statement is correct for the values of $f(x)$ ? $\newline$ A) The values of $f(x)$ for all even values of $x$ is the same. $\newline$ B) The value of $f(x)$ for all odd values of $x$ is the same. $\newline$ C) The value of $f(x)$ for all even values is $f(x)$ $0$ and for all odd values is $f(x)$ $1$ $\newline$ D) The value of $f(x)$ is either $f(x)$ $0$ or $f(x)$ $1$

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Math Problems

Algebra 1

Write two-variable inequalities: word problems

Full solution

Q. For all integers

x>0

, let

f(x)

be defined as

f(x)=\frac{f(x-1)}{(-1)^x}

. If

f(1)=1

, which of the following statement is correct for the values of

f(x)

\newline

A) The values of

f(x)

for all even values of

x

is the same.

\newline

B) The value of

f(x)

for all odd values of

x

is the same.

\newline

C) The value of

f(x)

for all even values is

f(x)

0

and for all odd values is

f(x)

1

\newline

D) The value of

f(x)

is either

f(x)

0

f(x)

1

Define Function: Define the function based on the given recursive formula and initial condition. Calculate $f(2)$ using $f(1)$ . $f(2) = f(1) / (-1)^2 = 1 / 1 = 1$ .
Calculate $f(2)$ : Calculate $f(3)$ using $f(2)$ . $f(3) = \frac{f(2)}{(-1)^3} = \frac{1}{-1} = -1$ .
Calculate $f(3)$ : Calculate $f(4)$ using $f(3)$ . $f(4) = f(3) / (-1)^4 = -1 / 1 = -1$ .