MATHEMATICS HIGH SCHOOL

Use the functions f(x) = 5x − 12 and g(x) = 11x + 2 to complete the function operations listed below. Part A: Find (f +g. (x). Show your work. (3 points) Part B: Find (f ⋅
g. (x). Show your work. (3 points) Part C: Find f[g(x)]. Show your work. (4 points)

Answers

Answer 1
Answer:

Answer:  The completed function operations are :

(f+g)(x)=16x-10,\n\n(f.g)(x)=55x^2-122x-24,\n\nf[g(x)]=55x-2.

Step-by-step explanation:  We are given two functions as follows :

f(x)=5x-12,\n\ng(x)=11x+2.

We are to complete the following function operations.

Part A : (f + g)(x)

We have

(f+g)(x)\n\n=f(x)+g(x)\n\n=(5x-12)+(11x+2)\n\n=16x-10.

Part B : (f . g)(x)

We have

(f.g)(x)\n\n=f(x).g(x)\n\n=(5x-12).(11x+2)\n\n=55x^2+10x-132x-24\n\n=55x^2-122x-24.

Part C : f[g(x)]

We have

f[g(x)]\n\n=f(11x+2)\n\n=5(11x+2)-12\n\n=55x+10-12\n\n=55x-2.

Thus, the completed function operations are :

(f+g)(x)=16x-10,\n\n(f.g)(x)=55x^2-122x-24,\n\nf[g(x)]=55x-2.
Answer 2
Answer: (f+g)(x)=f(x)+g(x)\n(f\cdot g)(x)=f(x)\cdot g(x)\n\nA.\n(f+g)(x)=5x-12+11x+2=16x-10\n\nB.\n(f\cdot g)(x)=(5x-12)(11x+2)\n(f\cdot g)(x)=55x^2+10x-132x-24\n(f\cdot g)(x)=55x^2-122x-24\n\nC.\nf(g(x))=5(11x+2)-12=55x+10-12=55x-2

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