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Indicate all correct alternatives if, f(...

Indicate all correct alternatives if, `f(x) = x/2-1`, then on the interval `[0, pi]`

A

tan `f(x)` and `(1)/(f(x))` are continuous

B

`tanf(x) and (1)/(f^(-1)(x))` are continuous

C

tan `f(x)` and `(1)/(f(x))` are continuous

D

`tan f(x)` is continuous but `(1)/(f(x))` is not continuous

Text Solution

Verified by Experts

The correct Answer is:
C, D
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Knowledge Check

  • If f(x) =1/2 x-1 , then on the interval [0,pi]

    A
    tan [f (x)] and 1/f (x) are both continuous
    B
    tan [f (x)] and 1/f (x) are both discontinuous
    C
    tan [f (x)] and `f^(-1)(x)` are both continuous
    D
    tan [f (x]] is discontinuous but 1/f (x) is not.

  • If f (x) = 1/2 x - 1 , then on the interval [0, pi]

    A
    tan [f(x)] and 1/f (x) are both continuous
    B
    tan [f(x)] and 1/f (x) are both discontinuous
    C
    `tan [f (x)] and f^(-1) (x)` are both continuous
    D
    tan [f (x)] is continuous but 1/f (x) is not continuous

  • The maximum value of f(x) =2 sin x + sin 2x , in the interval [0, (3)/(2)pi] is

    A
    `sqrt2 + 1`
    B
    `2 sqrt3`
    C
    `(3 sqrt3)/(2)`
    D
    `sqrt3`

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