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A function is continuous and differentiable on `R_0` satisfying `x f^(prime)(x)+f(x)=1 forall x` in its domain. If `f(1)=2`, then range of function does not contain

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Knowledge Check

  • Let f be the continuous and differentiable function such that f(x)=f(2-x), forall x in R and g(x)=f(1+x), then

    A
    g(x) is an odd function
    B
    f(x) is an even function
    C
    f(x) is symmetric about x=1
    D
    None of the above

  • The function f (x)=1/x on its domain is

    A
    increasing
    B
    decreasing
    C
    constant
    D
    information insufficient

  • A continuous and differentiable function f satisfies the condition, int_(0)^(x)f(t)dt=f^(2)(x)-1 for all real x. Then

    A
    f is monotonic increasing `AA x in R`
    B
    f is monotonic decreasing `AA x in R`
    C
    f is non monotonic
    D
    the graph of `y=f(x)` is a straight line

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