SOLUTION: Suppose that the functions r and s are defined for all real numbers x as follows. r(x)=4x-2 S(x)=x+3 Write the expressions for (s*r)(x) and (s-r)(x) and evaluate (s+r)(3)

Algebra ->  Functions -> SOLUTION: Suppose that the functions r and s are defined for all real numbers x as follows. r(x)=4x-2 S(x)=x+3 Write the expressions for (s*r)(x) and (s-r)(x) and evaluate (s+r)(3)      Log On


   

Question 1125997: Suppose that the functions r and s are defined for all real numbers x as follows.
r(x)=4x-2
S(x)=x+3
Write the expressions for (s*r)(x) and (s-r)(x) and evaluate (s+r)(3)
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
r%28x%29=4x-2
s%28x%29=x%2B3
Write the expressions for
%28s%2Ar%29%28x%29=+s%28x%29%2Ar%28x%29
%28s%2Ar%29%28x%29=%28x%2B3%29%284x-2%29
%28s%2Ar%29%28x%29=4x%5E2+%2B+10x+-+6

and
%28s-r%29%28x%29=s%28x%29-r%28x%29
%28s-r%29%28x%29=x%2B3-%284x-2%29
%28s-r%29%28x%29=x%2B3-4x%2B2
%28s-r%29%28x%29=-3x%2B5


evaluate %28s%2Br%29%283%29

to do it, first find %28s%2Br%29%28x%29

%28s%2Br%29%28x%29=s%28x%29%2Br%28x%29
%28s%2Br%29%28x%29=x%2B3%2B%284x-2%29
%28s%2Br%29%28x%29=x%2B3%2B4x-2
%28s%2Br%29%28x%29=5x%2B1
then
%28s%2Br%29%283%29=5%2A3%2B1
%28s%2Br%29%283%29=16