SOLUTION: For f(x)=x^2-3x-4, and g(x)=x-4... Evaluate and simplify the following: a) for what x, is f(x)=g(x)? b) (f-g)(x) c) (f/g)(x) Thank you for your time!

Algebra ->  Functions -> SOLUTION: For f(x)=x^2-3x-4, and g(x)=x-4... Evaluate and simplify the following: a) for what x, is f(x)=g(x)? b) (f-g)(x) c) (f/g)(x) Thank you for your time!      Log On


   

Question 752930: For f(x)=x^2-3x-4, and g(x)=x-4...
Evaluate and simplify the following:
a) for what x, is f(x)=g(x)?
b) (f-g)(x)
c) (f/g)(x)


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

For f%28x%29=x%5E2-3x-4, and g%28x%29=x-4
Evaluate and simplify the following:
a) for what x, is f%28x%29=g%28x%29?
x%5E2-3x-4=x-4....solve for x
x%5E2-3x%2Bx-4%2B4=0
x%5E2-2x=0...factor
x%28x-2%29=0...use zero product rule
solutions:
highlight%28x=0%29
if x-2=0 => highlight%28x=2%29


b)
%28f-g%29%28x%29=f%28x%29-g%28x%29
%28f-g%29%28x%29=x%5E2-3x-4-%28x-4%29
%28f-g%29%28x%29=x%5E2-3x-4-x%2B4
%28f-g%29%28x%29=x%5E2-4x

c)
%28f%2Fg%29%28x%29=f%28x%29%2Fg%28x%29
%28f%2Fg%29%28x%29=%28x%5E2-3x-4%29%2F%28x-4%29...write -3x+ as x-4x

%28f%2Fg%29%28x%29=%28x%5E2%2Bx-4x-4%29%2F%28x-4%29..group

%28f%2Fg%29%28x%29=%28%28x%5E2%2Bx%29-%284x%2B4%29%29%2F%28x-4%29

%28f%2Fg%29%28x%29=%28x%28x%2B1%29-4%28x%2B1%29%29%2F%28x-4%29

%28f%2Fg%29%28x%29=%28%28x-4%29%28x%2B1%29%29%2F%28x-4%29

%28f%2Fg%29%28x%29=%28cross%28%28x-4%29%29%28x%2B1%29%29%2Fcross%28%28x-4%29%29

%28f%2Fg%29%28x%29=x%2B1