Question

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Answer 1

Answer:

ur answer is: option (2)

explanation;

the given function is:

f(x)=sin^-1x + cos^-1x + tan^-1x

.we know that ,

sin^-1x and cos^-1x is defined when

x € [-1,1]

also, tan^-1x is defined when

x€R

thus, the given function f(x) will be defined when,

x€[-1,1]nR

ie, x€[-1,1]

thus, the function will be reduced to,

f(x)=sin^-1x + cos^-1x + tan^-1x

where,x€[-1,1]

ie, f(x)= π/2 + tan^-1x

where,x€[-1,1]

{since, sin^-1x + cos^-1x =π/2}

now, the function f(x) will be maximum at x=1 and minimum at x=-1.

thus , the maximum value of f(x) will be,

[f(x)]max.= π/2 + tan^-1(1)

= π/2 + π/4

= 3π/4

also,

[f(x)]min.= π/2 + tan^-1(-1)

= π/2 - tan^-1(1)

= π/2 - π/4

= π/4

hence, the range of the function f(x) is;

range (f) = [ π/4 , 3π/4 ]

thank you