f ( x ) = c o s ( π x ) , x ≠ 0 increases in the interval Options: A . &nbsp ( 1 2 k + 1 , 1 2 k ) B . &nbsp ( 1 2 k + 2 , 1 2 k + 1 ) C . &nbsp ( 1 2 k + 1 , 1 2 k + 3 ) D . &nbsp ( 1 2 k + 1 , 1 2 k + 3 )

Answer: Option A : A f(x) = cos ( π x ) Thus f(x) = cos ( π x ) increases in 1 3 → 1 2 generalizing it ( 1 2 k + 1 , 1 2 k )

f(x) = cos (πx), x ≠ 0 increases in the interval

Question -

$f (x) = c o s (\frac{π}{x}), x \neq 0$ increases in the interval

Options:

A .

(\frac{1}{2 k + 1}, \frac{1}{2 k})

B .

(\frac{1}{2 k} + 2, \frac{1}{2 k} + 1)

C .

(\frac{1}{2 k} + 1, \frac{1}{2 k} + 3)

D .

(\frac{1}{2 k + 1}, \frac{1}{2 k} + 3)

Answer: Option A
:
A
f(x) = cos

(\frac{π}{x})

Thus
f(x) = cos

(\frac{π}{x})

increases in

\frac{1}{3} \to \frac{1}{2}

generalizing it

(\frac{1}{2 k + 1}, \frac{1}{2 k})

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