SOLUTION: Can someone check my work. You can't imagine how grateful I am to this site and to all of the tutors. I am able to see step by step my mistakes. thank you. state the domain...I

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Question 91997: Can someone check my work. You can't imagine how grateful I am to this site and to all of the tutors. I am able to see step by step my mistakes. thank you.
state the domain...I think I have it...maybe
f(x) = sq rt x+4
x + 4 = 0 - 4
x = -4 is the domain???
g(x) = 2x+1/x-3
x-3= 0
x - 3 = 0 + 3
x = 3
h(x)= 3x^2 + 5x - 3
all of the numbers are real, correct?
or
9x + 5x -3
14x-3 = 0
that's not right

l(x) = 2x + 3
D = all real numbers
m(x) = 3/x^2 + 7
x + 7 = 0
x + 7 = 0 - 7
x = -7

Found 2 solutions by stanbon, jim_thompson5910:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
state the domain...I think I have it...maybe
f(x) = sqrt(x+4)
x=4 must be >=0
x must be >= -4
Domain: all Real Numbers >=-4
----------------------
g(x) = 2x+1/x-3
The denominator must not be zero.
Domain: all Real Numbers except x=3
---------------------------------
l(x) = 2x + 3
Domain: all real numbers
That's correct.
----------------------
m(x) = 3/(x^2 + 7)
The denominator must not be zero.
It never is because x^2 >=0 so x^2+7>=7.
Domain: all Real Numbers
----------------
================
Cheers,
Stan H.

Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!

Set the radicand (everything in the square root) greater than zero (remember you cannot take the square root of a negative number)

Subtract 4 from both sides

So the domain is x can be any number greater than -4

Set the denominator equal to zero

Add 3 to both sides. So x=3 is excluded from the domain since it makes the denominator equal to zero

So x can be any number except 3

you are correct, x can be any real number

l(x) = 2x + 3
you are correct, x can be any real number

Set the denominator equal to zero

Subtract 7 from both sides

Since you cannot take the square root of a negative and get a real answer, there are no values of x that will make equal zero. So the domain is x is an element of all real numbers