Mathematics

Problem

Let

k

be a non–zero real constant and consider the function

f:\mathbb R\setminus\{0\}\to\mathbb R

defined by

f(x)=\dfrac{k}{x}

. a. (i) State the domain of

f

. b. (ii) Prove that

0

does not belong to the range of

f

. c. (iii) Define a new function

g

g(x)=\dfrac{k}{x}+3

. Determine the range of

g

and give a reason for the value that is excluded.