Solved Problems

Tag: function

  • Problem 2-6: Odd and Even Functions

    Problem 2-6: Odd and Even Functions

    Which one of the following functions are even or odd or neither?
    a) \sin(x)
    b) \cos(x)
    c) \sin(x)\cos(x)
    d) x \sin(x)
    e) x^2
    f) \sin(x) + \cos(x)

    Recall that a function is said to be even if f(-x)=f(x) and odd if f(-x)=-f(x).

    Solution
    a) Odd \sin(-x)=-\sin(x)

    b) Even \cos(-x)=\cos(x)

    (more…)

  • Problem 2-1: Linearity of Functions

    Which one(s) of the following functions is linear?

    a) y=x+1.
    b) y=2x+1.
    c) y=1.
    d) y=x^2+x+1.
    e) y=x^1+1.
    f) y=\frac{1}{x}.
    g) y=\sin(x).

    h) y=\sqrt{x}.
    i) y=x+\frac{1}{1-x}.

    j) 5x+2y-1=0.
    k) y=x+c^2. ( c is an arbitrary constant).

    Solution
    a) Linear
    b) Linear
    c) Linear
    d) Nonlinear
    e) Linear
    f) Nonlinear

    g) Nonlinear
    h) Nonlinear
    i) Nonlinear
    j) Linear

    k) Linear