Mathematics

Problem

Define the function

h:\,D\to\mathbb{R}

h(x)=\dfrac{1}{x}

, where the domain is the union of two intervals

D=[-5,-1]\cup[1,4].

Answer the following questions. a. (i) Compute the values

h(-5),\, h(-1),\, h(1)

and

h(4)

. b. (ii) Using the nature of

h

on each sub-interval of

D

, obtain the complete range of

h

. c. (iii) Represent the range found in part (ii) on a number line. d. (iv) Decide, with reasons, whether

y=0.25

and

y=-2

can be values of

h(x)

for some

x\in D