Page 50 - Math SL HB Sem 1

r.U NCTIO NS, I.]Q TJ,.\'I'I ONS, IN IiQ I J A I, I'I'I ES

'I'YPF],S OF FI,]N(]'I'I0NS

I. (]OMPOSITE TTt]NCTION

Il/ is a function from set X to set I' and g is a lunction from sct I/ to set Z, thc
g(f(x)) is the composite function of I follow by g lrom X to Z and denoted by gol
The domain of gorf
lf r, c-d rlhen rt = tlJ l 1
d
'l'he
domain of /og
lf r c,l.then d. = dg
t- I tit: lir ) \,)l

The condition for the existence oIcomposite functions
For fog to be defined, r^ c-c1,
For gtl to be defined, r, cd*

)(xarn ple I

Given that f(i- .[r-i ancl g(r) -lnx. Does /og exist. [fso, define lully thc firnction
fog. Ifnot find a suitable restriction on thc domain ofg so that/crg exists.

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