Tag Archives: function

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