Question

Is the function $f\left(x\right)=\frac{(1+2^x{)}^2}{2^x}$odd or even

• A. Odd
• B. Even
• C. Neither even nor odd
• D. Even for some values of $x$

Answer 1

The correct option is B Even

$f\left(x\right)=\frac{(1+2^x{)}^2}{2^x}$
$f(-x)=\frac{(1+2^{-x}{)}^2}{2^{-x}}$
$f(-x)=\frac{(1+2^x{)}^2}{2^x}$
$\Rightarrow f(-x)=f\left(x\right)$
Hence, $f$ is even.