SOLUTION: for f(x)=4x and g(x)=^4-8, find each of the following a. (g*f)(-2) b. (f*g)(2) c. (g*f)(x) simplify d. (f*g)(x) simplify

Algebra ->  Functions -> SOLUTION: for f(x)=4x and g(x)=^4-8, find each of the following a. (g*f)(-2) b. (f*g)(2) c. (g*f)(x) simplify d. (f*g)(x) simplify      Log On


   

Question 965270: for f(x)=4x and g(x)=^4-8, find each of the following
a. (g*f)(-2)
b. (f*g)(2)
c. (g*f)(x) simplify
d. (f*g)(x) simplify
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

f%28x%29=4x and g%28x%29=x%5E4-8
a. %28g%2Af%29%28-2%29
since %28f%2Ag%29%28x%29=f%28x%29%2Ag%28x%29, you are multiplying the functions:
%28f%2Ag%29%28-2%29=4x%2A%28x%5E4-8%29
%28f%2Ag%29%28-2%29=4x%5E5-32x%29
%28f%2Ag%29%28-2%29=4%28-2%29%5E5-32%28-2%29%29
%28f%2Ag%29%28-2%29=4%28-32%29%2B64
%28f%2Ag%29%28-2%29=-128%2B64


b. %28f%2Ag%29%282%29
%28f%2Ag%29%282%29=4x%2A%28x%5E4-8%29
%28f%2Ag%29%282%29=4x%5E5-32x%29
%28f%2Ag%29%282%29=4%282%29%5E5-32%28-2%29%29
%28f%2Ag%29%282%29=4%2832%29%2B64
%28f%2Ag%29%282%29=128%2B64
%28f%2Ag%29%282%29=192


c. %28g%2Af%29%28x%29 simplify
%28f%2Ag%29%28x%29=4x%2A%28x%5E4-8%29
%28f%2Ag%29%28x%29=4x%5E5-32x%29

d. %28f%2Ag%29%28x%29=> will be same as c. by commutative property of multiplication