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

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