Consider the function defined by for all real for which it is defined.

MATHEMATICS · Multi-part · AP · AP Precalculus · Polynomial and Rational Functions · Polynomial and Rational Functions

Problem

Consider the function

g

defined by

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

for all real

x

for which it is defined. (i) Determine the domain of

g

. (ii) Solve

y=g(x)

for

x

and hence find the range of

g

. (iii) Find all real numbers

x

satisfying

g(x)=1

and those satisfying

g(x)=-2

. (iv) Verify that the product of the two

x

-values obtained in part (iii) is a constant independent of the chosen equation

(g(x)=1

g(x)=-2)