Use the functions a(x) = 4x + 9 and b(x) = 3x − 5 to complete the function operations listed below. Part A: Find (a + b)(x). Show your work. (3 points) Part B: Find (a ⋅ b)(x). Show your work. (3 points) Part C: Find a[b(x)]. Show your work. (4 points)
Step-by-step explanation:
Parts a and b are straight-forward. You add them in part a: 4x + 9 + 3x – 5 and you get 7x + 4. For part b, you are multiplying them (4x + 9)(3x – 5) by FOILing them: 12 x^{2} -20x+27x-4512x
2
−20x+27x−45 which simplifies to 12 x^{2} +7x-4512x
2
+7x−45
The last one is a composite; you are told to find a of b of x. The way you do that is to take your inside function and put that whole function into the other function every place you see an x, like this:
a(b(x))= 4(3x-5) + 9. Now distribute the 4 into the parenthesis to get 12x – 20 + 9, which simplifies to 12x – 11. And that’s it!