The period of the function $f(x)=10^{(\cos^2πx+x-[x])}+\sin^2πx$ is, ([x] represents greatest integer function)
Answer & explanation
Correct answer: option 1
$f(x)=10^{\{\cos^2πx+x-[x]\}}+\sin^2πx$
Now, $\cos^2π(x+1)=\cos^2(πx+π)$
$= \cos^2πx$
and $x +1−[x +1] = x −[x]$ [in fact $f (x + 2) = f (x); f (x + 3) = f (x)$ etc.]
∴ period of f (x) is 1.