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The period of the function $f(x)=10^{(\cos^2πx+x-[x])}+\sin^2πx$ is, ([x] represents greatest integer function) |
1 2 3 $π$ |
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. |
