+1800 Suppose $a(x) = 2x + 5 - 3x^2 + x^3$ and $b(x) = 4 - x^2 + 4x^4$. Find $(a\circ b)(3) - (b\circ a)(3).$
+1952 First, let's note that (a⋅b)(3)=a(b(3))
Now, we just work from inside to outside. We have
b(3)=4−(3)2+4(3)4=−5+324=319a(319)=2(319)+5−3(319)2+(319)3=32,157,119
We do the same exact thing with the second part of the equation. We get
(b⋅a)(3)=b(a(3))a(3)=2(3)+5−3(3)2+33=11b(11)=4−(11)2+4(11)4=58447
We have the two values needed now. All we have to do is to subtract them. We get
(a°b)(3)−(b°a)(3)=32,157,119−58447=32,098,672
So 32,098,672 is our final answer!
Thanks! :)
