Consider the function defined for all real .

MATHEMATICS · Multi-part · AoPS · Mathematics · Functions · Functions

Problem

Consider the function

g(x)=\dfrac{3}{x+2}-1

defined for all real

x\neq-2

. (i) Write the domain of

g

. (ii) Let

y=g(x)

. Express

x

in terms of

y

and simplify your expression. (iii) Using the expression obtained in part (ii), determine all real values that

y

can take, and hence write the range of

g