how do i find the domain of f(x)=|x+1|?

Question

Help Please. Step by Step answer please

Answer 1

how do i find the domain of f(x)=|x+1|?

 

The domain means all the legal values of x. Frequently this is the set of real numbers. But some functions have restrictions on the domain to prevent division by zero. For example:

 

           7

f(x) = ------

         x - 3

 

Here, the domain (possible values for x) are all real numbers except 3, because at 3 the function would be undefined - it would be 7/0 - a mathematical impossibility!

 

For your problem, you want to know what values for x can you plug in to the function to determine the resultant value f(x). So the domain is the set of real numbers.

Answer 2

Greetings Alexis!

Any time you encounter absolute values, that is short hand for saying you have a piece-wise function, or two functions put together. In essence, the function you've been given is shorthand for:

f(x) = -(x+1) = -x-1 for x+1<0 --> x<-1

AND

f(x) = +(x+1) = x+1 for x+1>=0 --> x>=-1

If that all seems too cluttered, just notice that all I am doing is taking the function inside the absolute value, and multiplying it by -1 for any value of x that makes it negative. I am leaving it alone otherwise.

Now you can see that |x+1| is a "downhill" line when x is less than -1, and an "uphill" line when x is greater than or equal to -1. No matter what the case, however, |x+1| is defined for all values of x, therefore the domain is all real numbers.

I know I went into some gory details there, but hopefully it has made absolute values a little less mysterious. They are quite possibly one of the strangest concepts to grasp in algebra.