Mathematics

Problem

Let

h: \mathbb R\setminus\{2\}\,\to\,\mathbb R

be defined by

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

. (i) Evaluate

h(4),\;h(1)

and

h\!\left(\dfrac52\right)

. (ii) Find all real numbers

x

for which

h(x)=\dfrac13

. (iii) From the set

\{2,3,5\}

identify those elements which do not have images under

h

and state the reason. (iv) Determine all real

x

for which the image

h(x)

is negative. a. a.