# 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 $\cos(-x)=\cos(x)$

# 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