Question

The maximum possible domain $D_f$ and the corresponding range $R_f$ of $f\left(x\right)=(-1{)}^x$ are

• A. $D_f=R$
• B. $R_f=\{-1,1\}$
• C. $D_f=Z$
• D. $R_f=[-1,1]$

Answer 1

Answer: (B), (C)

The correct options are
B $R_f=\{-1,1\}$
C $D_f=Z$

$f\left(x\right)=(-1{)}^x$ is defined when $x$ is an integer.
When $x$ is not an integer then we have multiple outputs. So it will not be a function.
For example, $f\left(\frac{1}{3}\right)=(-1{)}^{\frac{1}{3}}=-1$ or $-\omega$ or $-{\omega }^2$
$\therefore D_f=Z$ and $R_f=\{-1,1\}$