Let be the function defined by for all permissible real values of

MATHEMATICS · Multi-part · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

Let

h

be the function defined by

h(x)=\dfrac{2}{x-1}-4

for all permissible real values of

x

. Answer the following questions. (i) Find the domain of

h

. (ii) Show that

y=-4

is never attained by

h(x)

. (iii) Determine the complete range of

h

. (iv) Solve the inequality

h(x)>-2

and interpret your answer on the number line. (v) Using the information obtained above, sketch the graph of

h

in the

xy

–plane.