precalculus 12 grade

Question

Given tree function , which expression equal (k o b o z) (x)?

b(x)=9x , k(x)=x^4-2, z(x)=I5xI

answers I 5((9x)^4-2)I

(9I5xI^4)-2

I5(9(x^4-2))I

5(9x)^4I-2

Answer 1

Work backward. Put z in b.

9|5x|

Now put that inside k.

(9|5x|^4) - 2

Answer 2

First time I ever heard of function compositions as "tree functions" but, the way it works is that you start with the one on the far right, which is "z". So, taking "z" which is "|5x|" you plug that into "b" wherever there is an "x" in "b". So it becomes "9|5x|". Then you take that result and plug it into "k" wherever you see an "x" in "k". So it becomes (9|5x|)⁴ - 2.