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f(x)=sin^(-1)(sin x), g(x)=cos^(-1)(cos ...

`f(x)=sin^(-1)(sin x), g(x)=cos^(-1)(cos x)`, then :

A

`f(x)=g(x)" if " x in (0, (pi)/(4))`

B

`f(x) lt g(x)" if " x in ((pi)/(2), (3pi)/(4))`

C

`f(x) lt g(x)" if " (pi, (5pi)/(4))`

D

`f(x) gt g(x)" if " x in (pi, (5pi)/(4))`

Text Solution

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The correct Answer is:
A, B, C
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Knowledge Check

  • If f(x)=sin^(-1)(sin x),g(x)=cos^(-1)(cos x) and h(x)=cot^(-1)(cot x) , then which of the following is/are correct ?

    A
    `f(x)=g(x)=h(x)AA x in((pi)/(4),(pi)/(3))`
    B
    `f(x)lt g(x)lt h(x)AA x in ((pi)/(2),pi)`
    C
    `h(x)gt g(x)gt f(x)AA x in((3pi)/(2),2pi)`
    D
    `f(x)gt g(x)` has no real solution

  • Let f(x) = sin^(-1)|sin x| + cos^(-1)( cos x) . Which of the following statement(s) is / are TRUE ?

    A
    `f(f(3)) = pi`
    B
    f (x) is periodic with fundamental period `2 pi`
    C
    f (x) is neither even nor odd
    D
    Range of f(x) is `[0,2pi]`

  • Let f(x)=sin^(-1)x and g(x)=cos^(-1)x , then which of the following statements are correct?

    A
    `{:"f(x)" gt"g(x),"if"x in (1/sqrt2,1]:}`
    B
    `{:"f(x)" lt"g(x),"if"x in [-1,1/sqrt2):}`
    C
    `{:"f(x)" gt"g(x),"if"x in (-1/sqrt2,1/sqrt2):}`
    D
    `{:"f(x)" lt"g(x),"if"x in [-1/sqrt2,1/sqrt2]:}`

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