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If int(dx)/(x^2+a x+1)=f(x(x))+c , then ...

If `int(dx)/(x^2+a x+1)=f(x(x))+c ,` then `f(x)` is inverse trigonometric function for `|a|>2` `f(x)` is logarithmic function for `|a|<2` `g(x)` is quadratic function for `|a|>2` `g(x)` is rational function for `|a|<2`

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Knowledge Check

  • If g is inverse of function f and f'(x)=sinx , then g'(x) =

    A
    `cosec{g(x)}`
    B
    `sin {g(x)}`
    C
    `(1)/(sin{g(x)})`
    D
    none of these

  • If f(x) = sgn (x) and g (x) = (1-x^2) ,then the number of points of discontinuity of function f (g (x)) is -

    A
    exact two
    B
    exactly three
    C
    finite and more than 3
    D
    infinitely many

  • Let f(x) be a function such that f(x), f'(x) and f''(x) are in G.P., then function f(x) is

    A
    constant
    B
    logarithmic
    C
    exponential
    D
    linear

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