Home
Class 12
MATHS
The function, f(x) = cos^(-1) (cos x) is...

The function, `f(x) = cos^(-1) (cos x)` is

A

discontinuous at infinitely many-points

B

everywhere differentiable such that f'(x)=1

C

not differentiable at `x=n pi, n in Z and f'(x)=1, x ne n pi`

D

not differentiable at `x=n pi, n in Z` and `f'(x)=(-1)^(n), x in (n pi,(n+1)pi), n in Z`

Text Solution

Verified by Experts

The correct Answer is:
D
The graph of the `f(x)=cos^(-1)` (cos x) as given in Fig.6
It is evident from the curve y=f(x) that f(x) is everywhere continuous but it is not differentiable `x=n, n in Z`
Also, `f'(x)=(-1)^(n), x in (n pi,(n+1)pi),"where "n in Z`
We can observe that f(x) is an even periodic function with period `2pi`.
Promotional Banner

Similar Questions

Explore conceptually related problems

Define the function, f(x)=cos^(-1) (cos x)-sin^(-1) (sin x)" in "[0,2pi] and find the area bounded by the graph of the function and the x-axis.

For the function f(x) = cos^(-1)x + cos ^(-1) x^(2) which of the following statements is/are true

The domain of the function f(x)=cos^(-1)(x-[x]) is

The domain of the function f(x) = cos ^(-1)((2-x)/(4)) is

The domain of the function f(x)= sqrt(cos x) is

The domain of the function f(x)=cos^(-1)(sec(cos^-1 x))+sin^(-1)(cosec(sin^(-1)x)) is

Fundamental period of the function f(x) = cos (sinx) + cos(cosx) is :