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

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


   



Question 1139592: Suppose that the functions r and s
are defined for all real numbers x as follows.
r(x)=x+2
s(x)=4x^2
Write the expressions for (r+s)(x) and (r-s)(x) and evaluate (r times s)(-2).

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

r%28x%29=x%2B2
s%28x%29=4x%5E2
Write the expressions for %28r%2Bs%29%28x%29 and %28r-s%29%28x%29 and evaluate +%28r+%2As%29%28-2%29.
%28r%2Bs%29%28x%29=x%2B2%2B4x%5E2
%28r%2Bs%29%28x%29=4x%5E2%2Bx%2B2....eq.1
%28r-s%29%28x%29=x%2B2%2B4x%5E2-4x%5E2
%28r-s%29%28x%29=-4x%5E2%2Bx%2B2.......eq.2

+%28r+%2As%29%28-2%29.....first find +%28r+%2As%29%28x%29

+%28r+%2As%29%28x%29=%28x%2B2%294x%5E2

+%28r+%2As%29%28x%29=4x%5E3%2B8x%5E2

then,

+%28r+%2As%29%28-2%29=4%28-2%29%5E3%2B8%28-2%29%5E2
+%28r+%2As%29%28-2%29=4%28-8%29%2B8%284%29
+%28r+%2As%29%28-2%29=-32%2B32
+%28r+%2As%29%28-2%29=0