Page 52 - Math SL HB Sem 1

FUNCt toNs, EQU,\t'tONS ,INEQUALITIES

3. INVERSI.] FI]N(]'TION

lf f : x -> y is a function that maps-r to l/, then thc inverse function *ritten as ,f-r is a
function that maps y back to x.

>
\.q F

l)ortr;rirr I Ilirrrric l.

{ltangc.7', ) { I)orrririn 1-, )

Thc concept ofan inverse requires that given a function, / , there exists an inverse

Function /-r , such that
, ,,,f ,xr)_, ,"1)G)
.f,,f = I = -t <), (-[.-f =(-f

For the inverse function, /-r , to exist, then
l. f must be a one to one lunction
2. (i) The domain ol / is equal to the range of / |
i'e' d, =r ,-,

(ii) The range of / is equal to the dornain of /-r

i.e. d
r-, =r ,
3. f(f-'(r))= = f'' (f(x))
*

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