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The largest interval lying in (-pi/2,pi/...

The largest interval lying in `(-pi/2,pi/2)` for which the function `[f(x)=4^-x^2+cos^(-1)(x/2-1)+log(cosx)]` is defined, is (1) `[0,pi]` (2) `(-pi/2,pi/2)` (3) `[-pi/4,pi/2)` (4) `[0,pi/2)`

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To determine the largest interval lying in \((- \frac{\pi}{2}, \frac{\pi}{2})\) for which the function \[ f(x) = 4^{-x^2} + \cos^{-1}\left(\frac{x}{2} - 1\right) + \log(\cos x) \] is defined, we need to analyze each component of the function. ...
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Knowledge Check

  • The largest interval lying in (-pi/2, pi/2) for which the function f(x) = 4^(-x^2) + cos^(-1)(x/2-1) + log (cosx) is deefind, is

    A
    `[0,pi]`
    B
    `(-pi/2,pi/2)`
    C
    `[-pi/4,pi/2)`
    D
    `[0, pi/2)`

  • The largest intervgal lying in (- pi/2, pi/2) for which the function [1f(x)=4^(-x^2) + cos^(-1) (x/2 -1) +log (cos x)] is defined, is :

    A
    `[0 ,pi]`
    B
    ` (- (pi)/(2) ,(pi)/(2))`
    C
    `[(-pi)/(4),(pi)/(2))`
    D
    `[0,(pi)/(2))`

  • The largest interval lying in ((-pi)/(2) , (pi)/(2)) for which the function [f(x) = 4^(-x^(2)) + cos^(-1) ((x)/(2) - 1) + log (cos x) ] is defined is -

    A
    –f(x)
    B
    f(x)
    C
    f(a) + f(a – x)
    D
    f(–x)