How do you find the compositions given #g(x) = 3x + 2# and #h(x) = 9x^2 + 12x + 9#?

1 Answer
mason m
Jan 4, 2016

#g(h(x))=27x^2+36x+29#
#h(g(x))=81x^2+144x+69#

Explanation:

Function compositions are basically plugging one function into another function.

To find #g(h(x))#, take #h(x)#, which is #9x^2+12+9#, and plug it into the #x# in #g(x)#.

#g(color(blue)(x))=3color(blue)x+2#
#h(x)=9x^2+12x+9#

#g(color(blue)(h(x)))=3color(blue)((9x^2+12x+9))+2#
#g(h(x))=27x^2+36x+27+2#
#g(h(x))=27x^2+36x+29#

To find #h(g(x))#, do the process with the roles switched: #g(x)# is plugged into #h(x)#.

#h(g(x))=9(3x+2)^2+12(3x+2)+9#
#h(g(x))=9(9x^2+12x+4)+36x+24+9#
#h(g(x))=81x^2+108x+36+36x+33#
#h(g(x))=81x^2+144x+69#

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