Page 62 - Math SL HB Sem 1

FUNCTIONS, E,QUAI'IONS, INEQUALITII'S

5. THE RECIPROCALFUNCTION

One intcresting lunction is /(x) . -l * , 0
,
.r

This graph has a shape known as a rectangular hyperbola. The horizontal and ve(ical
asymptotes of the basic function !, x * 0 can also be 'relocated'.
-tG) =
x
'I 1 ]
he inverse function ot f(x)= i, /-'(r)
xx , * * O,
r
i.e. .[(f (x))= x> I = x <> f a (x)= 1- Tt"n, as the rwo f -I(x) functions are identical, it is
I
its self-inverse-

Sketching the graph of f(x) =1 , x r 0 and reflecting it about the linc y - x will show that thc
x
two graphs overlap each other. v

I
x

x

Example I
Sketch the graph of the following function

a) f(x) = -l- -2
x-l
b)f(x)=2-?
x

3- li