SOLUTION: evaluate the following:and identify the domain Functions for the problem: f(x)= 2x^2+5x+7 and g(x)=x^3+2 1. (f+g)(x) 2. (f-g)(x) 3. (g.f)(x) 4. (f/g)(x)

Algebra ->  Functions -> SOLUTION: evaluate the following:and identify the domain Functions for the problem: f(x)= 2x^2+5x+7 and g(x)=x^3+2 1. (f+g)(x) 2. (f-g)(x) 3. (g.f)(x) 4. (f/g)(x)      Log On


   

Question 74672: evaluate the following:and identify the domain
Functions for the problem: f(x)= 2x^2+5x+7 and g(x)=x^3+2
1. (f+g)(x)
2. (f-g)(x)
3. (g.f)(x)
4. (f/g)(x)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
1.
You're simply going to add each like term from both equations
%28f%2Bg%29%28x%29=f%28x%29%2Bg%28x%29=%282x%5E2%2B5x%2B7%29%2B%28x%5E3%2B2%29
%28f%2Bg%29%28x%29=f%28x%29%2Bg%28x%29=x%5E3%2B2x%5E2%2B5x%2B9
Domain is all real numbers since the domain of the 2 equations is all real numbers.



2.
Now you're going to subtract like terms.
%28f-g%29%28x%29=f%28x%29-g%28x%29=%282x%5E2%2B5x%2B7%29-%28x%5E3%2B2%29
%28f-g%29%28x%29=f%28x%29-g%28x%29=-x%5E3%2B2x%5E2%2B5x%2B5
Domain is all real numbers since the domain of the 2 equations is all real numbers.


3.
Now you're going to multiply each equation
%28f%2Ag%29%28x%29=f%28x%29%2Ag%28x%29=%282x%5E2%2B5x%2B7%29%28x%5E3%2B2%29

%28f%2Ag%29%28x%29=f%28x%29%2Ag%28x%29=2x%5E5%2B4x%5E2%2B5x%5E4%2B10x%2B7x%5E3%2B14
%28f%2Ag%29%28x%29=f%28x%29%2Ag%28x%29=2x%5E5%2B5x%5E4%2B7x%5E3%2B4x%5E2%2B10x%2B14Rewrite terms in descending degree. Domain is all real numbers since the domain of the 2 equations is all real numbers.



4.
This time you're going to divide the 2 equations
%28f%2Fg%29%28x%29=f%28x%29%2Fg%28x%29=%282x%5E2%2B5x%2B7%29%2F%28x%5E3%2B2%29
%28f%2Fg%29%28x%29=f%28x%29%2Fg%28x%29=%282x%5E2%2B5x%2B7%29%2F%28x%5E3%2B2%29 And this is the simplest form since it cannot be reduced further. The domain is all real numbers except x cannot equal -root%283%2C2%29