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Question 142216: Could you please help me find the domain for these problems:
1. f(x)=3x-2
2. f(x)=4-2/x
3. f(x)=1/x4
4. f(x)=8/x+4 Thank you in advance for your help.
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! 1)
Looking at  , we can see that there are no square roots, logs, and other functions where there are restrictions on the domain.
Also, we can see that the function does not have a division by x (or any combination of variables and constants).
So we don't have to worry about division by zero.
Since we don't have any restrictions on the domain, this shows us that the domain is all real numbers. In other words, we can plug in any number in for x
So the domain of the function in set-builder notation is:
In plain English, this reads: x is the set of all real numbers (In other words, x can be any number)
Also, in interval notation, the domain is:
)
2)
 Start with the given function
 Set the denominator equal to zero. Remember, dividing by 0 is undefined. So if we find values of x that make the denominator zero, then we must exclude them from the domain.
Since makes the denominator equal to zero, this means we must exclude from our domain
So our domain is: 
which in plain English reads: x is the set of all real numbers except 
So our domain looks like this in interval notation
\cup\left(0,\infty \right))
note: remember, the parenthesis excludes 0 from the domain
If we wanted to graph the domain on a number line, we would get:
 Graph of the domain in blue and the excluded value represented by open circle
Notice we have a continuous line until we get to the hole at (which is represented by the open circle).
This graphically represents our domain in which x can be any number except x cannot equal 0
3)
 Start with the given function
 Set the denominator equal to zero. Remember, dividing by 0 is undefined. So if we find values of x that make the denominator zero, then we must exclude them from the domain.
 Take the fourth root of both sides
Simplify
Since makes the denominator equal to zero, this means we must exclude from our domain
So our domain is:
which in plain English reads: x is the set of all real numbers except
So our domain looks like this in interval notation
note: remember, the parenthesis excludes 0 from the domain
If we wanted to graph the domain on a number line, we would get:
Graph of the domain in blue and the excluded value represented by open circle
Notice we have a continuous line until we get to the hole at (which is represented by the open circle).
This graphically represents our domain in which x can be any number except x cannot equal 0
4)
 Start with the given function
 Set the denominator equal to zero. Remember, dividing by 0 is undefined. So if we find values of x that make the denominator zero, then we must exclude them from the domain.
 Subtract 4 from both sides
 Combine like terms on the right side
Since makes the denominator equal to zero, this means we must exclude from our domain
So our domain is: 
which in plain English reads: x is the set of all real numbers except 
So our domain looks like this in interval notation
\cup\left(-4,\infty \right))
note: remember, the parenthesis excludes -4 from the domain
If we wanted to graph the domain on a number line, we would get:
 Graph of the domain in blue and the excluded value represented by open circle
Notice we have a continuous line until we get to the hole at (which is represented by the open circle).
This graphically represents our domain in which x can be any number except x cannot equal -4
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