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True or False: The composition of functions is associative

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  • Let f(x) g(x) and h(x) be the three functions
  • Then composition of functions is associative if $ho(gof)=(hog)of$
$ho(gof)(x)=h(gof(x))$
 
$=h(g(f(x)) \forall x$
 
$(hog)of (x)=hog(f(x))$
 
$=h(g(f(x)))$
 
$ho(gof)(x)=(hog)of(x)$
 
Hence composition of function is associative
 
The given statement is 'True'

 

answered Mar 6, 2013 by meena.p
 

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