Mathematics

Problem

Let

g:[2,10]\to\mathbb{R}

be the function given by

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

. Carry out the tasks below. a. (i) Calculate the values

g(2)

g(5)

and

g(10)

. b. (ii) Using the fact that

g

is strictly decreasing on its domain, determine the greatest and least values of

g(x)

[2,10]

. c. (iii) Hence write the exact range of

g

in interval notation. d. (iv) Express the same result obtained in part (iii) as a single inequality involving

y