SOLUTION: 12 pts) Let f (x) = 3x2 + 4x - 8 and g(x) = 3 - 2x. a. Evaluate the function (g - f)(x) for x = - 4. That is, find (g - f)( - 4). Show work. b. Evalu

Algebra ->  Graphs -> SOLUTION: 12 pts) Let f (x) = 3x2 + 4x - 8 and g(x) = 3 - 2x. a. Evaluate the function (g - f)(x) for x = - 4. That is, find (g - f)( - 4). Show work. b. Evalu      Log On


   

Question 1134031: 12 pts) Let f (x) = 3x2 + 4x - 8 and g(x) = 3 - 2x.
a. Evaluate the function (g - f)(x) for x = - 4. That is, find (g - f)( - 4). Show work.




b. Evaluate the function (fg)(x) for x = - 4. That is, find (f g)( - 4). Show work.





c. Show the difference function (f - g)(x). Simplify the function as much as possible. Show work.




Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Let f+%28x%29+=+3x%5E2+%2B+4x+-+8+and+g%28x%29+=+3+-+2x.
a. Evaluate the function
%28g+-+f%29%28x%29 for+x+=+-+4. .....first find %28g+-+f%29%28x%29
%28g+-+f%29%28x%29=3+-+2x-%28+3x%5E2+%2B+4x+-+8%29
%28g+-+f%29%28x%29=3+-+2x-+3x%5E2+-+4x+%2B+8
%28g+-+f%29%28x%29=+-+3x%5E2+-+6x+%2B+11
no find find %28g+-+f%29%28+-+4%29:
%28g+-+f%29%28-4%29=+-+3%28-4%29%5E2+-+6%28-4%29+%2B+11
%28g+-+f%29%28-4%29=+-+3%2816%29+%2B+24+%2B+11
%28g+-+f%29%28-4%29=+-+48+%2B+35
%28g+-+f%29%28-4%29=+-13

b. Evaluate the function %28fg%29%28x%29 for x+=+-+4:
%28g+%2Af%29%28x%29=%283+-+2x%29%28+3x%5E2+%2B+4x+-+8%29
%28g+%2Af%29%28x%29=+9x%5E2+%2B+12x+-+24-6x%5E3-8x%5E2%2B16x
%28g+%2Af%29%28x%29=-6x%5E3%2B+x%5E2+%2B+28x+-+24
now find %28f+%2Ag%29%28+-+4%29:
%28g+%2Af%29%28-4%29=-6%28-4%29%5E3%2B+%28-4%29%5E2+%2B+28%28-4%29+-+24
%28g+%2Af%29%28-4%29=-6%28-64%29%2B+16+-112+-+24
%28g+%2Af%29%28-4%29=384%2B+16+-112+-+24
%28g+%2Af%29%28-4%29=264

c. Show the difference function %28f+-+g%29%28x%29. Simplify the function as much as possible. Show work.
%28g+-+f%29%28x%29=g%28x%29-f%28x%29
%28g+-+f%29%28x%29=%283+-+2x%29-%28+3x%5E2+%2B+4x+-+8%29
%28g+-+f%29%28x%29=3+-+2x-+3x%5E2+-+4x+%2B+8
%28g+-+f%29%28x%29=+-+3x%5E2+-+6x+%2B+11