SOLUTION: For the given functions f and​ g, complete parts​ (a)-(h). For parts​ (a)-(d), also find the domain. f(x)=x-3; g(x)=9x^2 a) Find (f+g)(x) What is the domain? b

Algebra ->  Average -> SOLUTION: For the given functions f and​ g, complete parts​ (a)-(h). For parts​ (a)-(d), also find the domain. f(x)=x-3; g(x)=9x^2 a) Find (f+g)(x) What is the domain? b      Log On


   

Question 1123467: For the given functions f and​ g, complete parts​ (a)-(h). For parts​ (a)-(d), also find the domain. f(x)=x-3; g(x)=9x^2
a) Find (f+g)(x) What is the domain?
b) Find (f-g)(x) What is the domain?
c) Find (f*g)(x) What is the domain?
d) Find (f/g)(x) What is the domain?
e) Find (f+g)(4)
f) Find (f-g)(3)
g) Find (f*g)(2)
h) Find (f/g)(2)
THANK YOU...sorry I typed the wrong number
Found 2 solutions by solver91311, MathLover1:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


The domain of a function is the set of values of the independent variable for which the function is defined. (your independent variable is in all cases presented here).

All of the functions you are dealing with here are either polynomial functions or rational functions. The domain of any polynomial function with real coefficients is the entire set of real numbers. The domain of any of the rational functions represented here is the set of all real numbers excluding any value that would cause a denominator to be zero.


John

My calculator said it, I believe it, that settles it

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

f%28x%29=x-3; g%28x%29=9x%5E2+
a) Find %28f%2Bg%29%28x%29 What is the domain?
%28f%2Bg%29%28x%29=f%28x%29%2Bg%28x%29
%28f%2Bg%29%28x%29=x-3%2B9x%5E2
%28f%2Bg%29%28x%29=9x%5E2%2Bx-3
domain: R (all real numbers)



b) Find %28f-g%29%28x%29 What is the domain?
%28f-g%29%28x%29=f%28x%29-g%28x%29
%28f-g%29%28x%29=x-3-9x%5E2
%28f-g%29%28x%29=-9x%5E2%2Bx-3
domain: R (all real numbers)


c) Find %28f%2Ag%29%28x%29 What is the domain?
%28f%2Ag%29%28x%29=%28x-3%299x%5E2
%28f%2Ag%29%28x%29=9x%5E3-27x%5E2
domain: R (all real numbers)


d) Find (f/g)(x) What is the domain?
%28f%2Fg%29%28x%29=%28x-3%29%2F%289x%5E2%29
%28f%2Fg%29%28x%29=x%2F%289x%5E2%29-3%2F%289x%5E2%29
%28f%2Fg%29%28x%29=1%2F%289+x%29+-+1%2F%283+x%5E2%29
domain:{ x element R : x%3C%3E0 }


e) Find %28f%2Bg%29%284%29
%28f%2Bg%29%28x%29=9x%5E2%2Bx-3....plug in 4 for x
%28f%2Bg%29%284%29=9%2A4%5E2%2B4-3
%28f%2Bg%29%284%29=145


f) Find %28f-g%29%283%29
%28f-g%29%28x%29=-9x%5E2%2Bx-3...plug in 3 for x
%28f-g%29%283%29=-9%2A3%5E2%2B3-3
%28f-g%29%283%29=-81


g) Find %28f%2Ag%29%282%29
%28f%2Ag%29%28x%29=9x%5E3-27x%5E2 ....plug in 2 for x
%28f%2Ag%29%282%29=9%2A2%5E3-27%2A2%5E2
%28f%2Ag%29%282%29=-36


h) Find %28f%2Fg%29%282%29
%28f%2Fg%29%28x%29=1%2F%289+x%29+-+1%2F%283+x%5E2%29....plug in 2 for x
%28f%2Fg%29%282%29=1%2F%289+%2A2%29+-+1%2F%283+%2A2%5E2%29

%28f%2Fg%29%282%29=1%2F18+-+1%2F12
%28f%2Fg%29%282%29=-1%2F36