SOLUTION: I missed the day of class when we covered domains in my class, and now i am hopelessly lost. Please help me solve the following problems, and explain how you did it. I am not ve

Question 166656: I missed the day of class when we covered domains in my class, and now i am hopelessly lost.
Please help me solve the following problems, and explain how you did it. I am not very good at math, so the more you can break it down and explain it, the better.
find the domain of the rational function:
h(t)=(t-5)/(t^2-25)

g(x)=(x^3-27)/(4x)

the problems are written in faction form, but I don't know how to do that with the computer, so I am not sure if what i have written means the same thing. It should read t-5 over t^2-25.
I would really appreciate the help!
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Remember, the domain is simply the set of all x values that produce a y value.

# 1

Start with the given function

Set the denominator equal to zero. Remember, dividing by 0 is undefined. So if we find values of "t" that make the denominator zero, then we must exclude them from the domain.

Factor the left side (note: if you need help with factoring, check out this solver)

Now set each factor equal to zero:

or

or Now solve for t in each case

So our solutions are or

Since and make the denominator equal to zero, this means we must exclude and from our domain

So our domain is:

which in plain English reads: t is the set of all real numbers except t CANNOT equal or t CANNOT equal

So our domain looks like this in interval notation

note: remember, the parenthesis excludes -5 and 5 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 values represented by open circles

Notice we have a continuous line until we get to the holes at and (which is represented by the open circles).
This graphically represents our domain in which t can be any number except t cannot equal -5 or 5

# 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.

Divide both sides by 4 to isolate x

Divide

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 x CANNOT equal

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

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