Page 52 - Math SL HB Sem 1

I,'T]NC]]'IONS, E QLIATIONS, INEQUALI'tIES

3. INVERSEFUNCTION

lf :x-+ y is a function that maps jr to -1, , 15"n the inve rse function written as /-r isa
f
function that maps y back to x.

1'q p l' l

l't

I)rrrtr;rirr / ltirn:,.1c /'

'
{l<angc./ } {l lorrrain./ ,}

TIre concep{ ofan inverse requires that given a function, f , tbere exists an inverse
Function ,f-r , such that
, ,Xr)_r ,.J)6)
.f,,.f = I = [ ',,-f <), (_f.-f =(-f

For the inverse function, / r, to exist, then
I f must be a one to one function

2 (i) The domain of / is equal to the range of / I

i.e. d, =r
,,
(ii) The range of / is equal to the dornain of /-'
i.e. d, , -r ,
3. f(f-'(r))= = f'' (f(r))
r

l-6