How do you find #[fog](x)# and #[gof](x)# given #f(x)=1+x# and #g(x)=x^2+5x+6#?

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Answer 1 · 2017-02-13T15:32:35

# [fog ] (x)=x^2+5x+7#
# [ gof ] (x) =x^2+7x+12#

This is a composition of functions

#f(x)=1+x#

#g(x)=x^2+5x+6=(x+2)(x+3)#

# [ fog ] (x)=f(g(x))=f(x^2+5x+6)#

#=1+x^2+5x+6=x^2+5x+7#

#[ gof ] (x)=g(f(x))=g(1+x)=(x+2+1)(x+3+1)#

#=(x+3)(x+4)#

#=x^2+7x+12#

# [ fog ] (x) != [ gof ] (x)#