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the sum of max and min values of function f(x)=sin -1 2x+cos -1 2x+sec -1 2x is a) π b) π/2 c) 2 π d) 3 π/ 2

the sum of max and min values of function f(x)=sin-12x+cos-12x+sec-12x is


a) π


b) π/2


c) 2π


d) 3π/2

 


Grade:

3 Answers

AskIITian Expert Priyasheel - IITD
8 Points
11 years ago

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askiitian.expert- chandra sekhar
10 Points
11 years ago

Hi Anurag,

f(x)=sin-12x+cos-12x+sec-12x

sin-12x+cos-12x = π/2 for all x

sec-12x belongs to [0,π ]-{π/2}


therefore min of
sec-12x is 0

                   max of sec-12x is π


therefore min of f(x) is
π/2

                   max of f(x) is 3π/2


sum of min and max  values of f(x) is (
π/2 + 3π/2) = 2π


Ans: (c)

All the best

askiitian.expert- chandra sekhar

askIITianexpert IITDelhi
8 Points
11 years ago

As Sin-1x  & Cos-1x is defined for x belongs to[-1,1] . Sec-1x is defined for x≤-1 & x≥1.Also Sin-1x+Cos-1x=¶/2 in the domain specified.

Domain of above function f(x) is x={-1/2 , 1/2}   (By solving inequalities -1≤x≤1,x≤-1 & x≥1)

Hence max{f(x)}=¶/2+Sec-1 (2*1/2)=¶/2+¶/2=¶

while min{f(x)}=0.So their sum=¶       ;   Answer is (a).

 

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