SOLUTION: =/ Alright so i just got off of long term suspention cause someone decided to fight me and i had to defend myself and now im suspected to do this unit test tommorow i broke or else

Click here to see ALL problems on Rational-functions

Question 354852: =/ Alright so i just got off of long term suspention cause someone decided to fight me and i had to defend myself and now im suspected to do this unit test tommorow i broke or else id pay for a tutor could someone explain how to solve these problems for me ?
Solve the equation/ Check for extraneous solutions.
1.x^(1/2)+5=4
2.3(to the squar root of)2x+4=12
3.( cubed root of the Nth root or what ever) inside is x+40=-5
4.x-4= square root of 2x

a)erform the indicated operation
b) State the domain of the result
F(x)=3x and g(x)= x-5
5.F(x)+ g(x)
6.F(x)/G(x)
7.f(x)*g(x)
8.f(g(x))
Thats alll I need to know like i reviewed 20 problems i dont know and learnd them I cant get this anywhere and im running out of time
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Solve the equation/ Check for extraneous solutions.
1.x^(1/2)+5=4
x^(1/2) = -1
x = 1
----------------
2.3(to the squar root of)2x+4=12
3*sqrt(2x+4) = 12
sqrt(2x+4) = 4
2x+4 = 16
2x = 12
x = 6
-------
3.( cubed root of the Nth root or what ever) inside is x+40=-5
(x+40)^(1/3) = -5
x+40 = -125
x = -165
----------------
4.x-4= square root of 2x
x-4 = sqrt(2x)
(x-4)^2 = 2x
x^2 -8x + 16 = 2x
x^2 - 10x + 16 = 0
(x-2)(x-8) = 0
x = 2 or x = 8
----
Checking in the original equation you get
x = 2 but x cannot be 8
============================
a) perform the indicated operation
b) State the domain of the result
F(x)=3x and g(x)= x-5
5.F(x)+ g(x) = 3x+x-5 = 4x-5
Domain: All Real Numbers
-----------------------
6.F(x)/G(x) = 3x/(x-5)
Domain: All Real Numbers except x = 5
-----------------------
7.f(x)*g(x) = (3x)(x-5) = 3x^2-15x
Domain: All Real Numbers
------------------------
8.f(g(x)) = f(x-5) = 3(x-5) = 3x-15
Domain: All Real Numbers
===============================
Cheers,
Stan H.