Mathematics

Problem

Consider the function

g

given by

g(x)=\dfrac{3}{x-2}

with domain

\mathbb{R}\setminus\{2\}

. a. (i) Find the range of

g

. b. (ii) Determine

g^{-1}

and state its domain and range. c. (iii) Verify that

g(g^{-1}(y))=y

for every permissible

y