Home
Class 12
MATHS
Number of point where function f(x) defi...

Number of point where function f(x) defined as `f:[0,2pi] rarrR,f(x)={{:(3-|cosx-(1)/(sqrt2)|",",|sinx|lt(1)/(sqrt2)),(2+|cosx+(1)/(sqrt2)|",",|sinx|ge(1)/(sqrt2)):}` is non differentiable is

A

2

B

4

C

6

D

0

Text Solution

Verified by Experts

The correct Answer is:
B
`f(x)={{:(3-|cosx-(1)/(sqrt2)|",",|sinx|lt(1)/(sqrt2)),(2+|cosx+(1)/(sqrt2)|",",|sinx|ge(1)/(sqrt2)):}`
`" "={{:(3-|cosx-(1)/(sqrt2)|",",|sinx|gt(1)/(sqrt2)),(2+|cosx+(1)/(sqrt2)|",",|cosx|le(1)/(sqrt2)):}`
`" "={{:(3-cosx-(1)/(sqrt2)",",|cosx|gt(1)/(sqrt2)),(2+cosx+(1)/(sqrt2)",",|cosx|le(1)/(sqrt2)):}`
Thus, f(x) is discontinuous at `|cosx|=(1)/(sqrt2)` or
`x=(pi)/(4),(3pi)/(4),(5pi)/(4),(7pi)/(4)`
Promotional Banner

Topper's Solved these Questions

  • CONIC SECTIONS

    CENGAGE PUBLICATION|Exercise All Questions|102 Videos

  • COORDINATE SYSTEM

    CENGAGE PUBLICATION|Exercise Multiple Correct Answers Type|2 Videos

Similar Questions

Explore conceptually related problems

sinx + cosx = 1/sqrt(2)

sqrt(3) sinx + cosx = sqrt(2)

sinx + cosx = sqrt(2) cos2x

Evaluate: int_(0)^((pi)/(2))(sqrt(cosx))/(sqrt(sinx)+sqrt(cosx))dx

int_(0)^((pi)/(2))(dx)/(2cosx+4sinx)=(1)/(sqrt(5))log((3+sqrt(5))/(2))

int_0^(pi/2)(sqrt(sinx))/(sqrt(sinx)+sqrt(cosx)) dx

int_(0)^((pi)/(2))(xdx)/(sinx+cosx)=(pi)/(2sqrt(2))log(sqrt(2)+1)

if: f(x)=(sinx)/(sqrt(1+tan^2x))-(cosx)/(sqrt(1+cot^2x)), then find the range of f(x)

If int(sinx)/(sin(x-(pi)/(4)))dx=Af(x)+(1)/(sqrt2)log[|sinx-cosx|]+c, then

The number of integers in the range of the function f(x)=|4((sqrt(cos"x")-sqrt(sinx))(sqrt(cos"x")+sqrt(sinx)))/(cosx+sinx)| is______