Question

If $f\left(x\right)$ is an odd function then $\cos f\left(x\right)$ is

• A. even
• B. odd
• C. neither even nor odd
• D. a constant function

Answer 1

Answer: (A)

even

$\because$ $f\left(x\right)$ is an odd function
So, $f(-x)=-f\left(x\right)$
$F(-x)=\cos \left(f\right(-x\left)\right)$
$=\cos (-f(x\left)\right)$
$=\cos \left(f\right(x\left)\right)$
$=F\left(x\right)$
So $\cos \left(f\right(x\left)\right)$ is an even function