find domain for f(x)= 5x/x-5

Question

What is the domain for f(x)=5x/x-5?

Answer 1

Dezmond,

At the level of college algebra, we concern ourselves with two domain questions:

1) Is there some value(s) of x which would give the function a denominator of zero?  We must exclude these values from the domain since we cannot divide by zero.  This will create a "hole" in the domain.  To find these holes, simply set the denominator equal to zero and solve for the variable.  These numbers are excluded from the domain.

 

Ex:

f(x) = 1/(x+3/2)

Is there some x that will make the denominator zero?  It looks like it:

x + 3/2 = 0

x = -3/2

So the domain is (-∞,-3/2), (-3/2,∞)

A hole at x = -3/2

 

2) Do I have a variable showing up under an even-indexed radical expression within the function?  If so, I should take care that the domain only includes values for which there is only a non-negative number under the even-indexed radical.  To find the domain here, think about what we're saying:

"What is under the even-indexed radical must be non-negative."

How can we express that mathematically?  Here is an example:

f(x) = √(x+3/2)

x + 3/2 ≥ 0

x ≥ -3/2

So the domain is [-3/2,∞)

 

If you need additional help, I can provide it online or in-person since you are in Athens too.

Michael J