Let f(x) = log (sin x+ cos x), x in (-pi...

Let `f(x) = log (sin x+ cos x)`, `x in (-pi/4,(3pi)/(4))`
Then f is stricly increasing in the interval

A

(a) `(-pi/4,pi/4)`

B

(b) `(0,(3pi)/8)`

C

(c) `(pi/4,pi/2)`

D

(d) `(pi/2(3pi)/4)`

Verified by Experts

The correct Answer is:

A

Similar Questions

Explore conceptually related problems

If f(x) = x- sqrt x is increasing in the interval..

the function f(x)=logx/x is increasing in the interval

Let f(x) = (1-tanx)/(4x-pi), x != (pi)/4, x in [0,(pi)/2] . If f(x) is continuous in [0,(pi)/2] , then f((pi)/(4)) is

If {:(f(x),=(cos x - sin x)/(cos 2x),",", x != (pi)/4),(,=k, ",", x = (pi)/4):} is continous at x = (pi)/4 , then the value of k is

The function f(x)=sin^4x +cos ^4 x increases if

If f(x)=(e^(x)+e^(-x)-2)/(x sin x) , for x in [(-pi)/(2), (pi)/(2)]-{0} , then for f to be continuous in [(-pi)/(2), (pi)/(2)], f(0)=

Let f(x) = {((tan x - cot x)/(x-pi/4), ",", x != pi/4),(a, ",", x = pi/4):} The value of a so that f(x) is continuous at x = (pi)/4 , is

cos((3pi)/4+x)-cos((3pi)/4-x)=

If f(x) =cos [pi^(2)]x+ cos [-pi^(2)] x, where [x] denots the greatest integer function, then the value of f((pi)/(2)) is-