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

Related questions
See all questions in Function Composition
Impact of this question
1921 views around the world
You can reuse this answer
Creative Commons License