SOLUTION: State the domain for the function: f(x) = x/(x + 1) A. {x: all real numbers} B. {x: all real numbers except 0} C. {x: all real numbers except –1} D. {x: all real num

Algebra ->  Functions -> SOLUTION: State the domain for the function: f(x) = x/(x + 1) A. {x: all real numbers} B. {x: all real numbers except 0} C. {x: all real numbers except –1} D. {x: all real num      Log On


   

Question 316365: State the domain for the function: f(x) = x/(x + 1)

A. {x: all real numbers}
B. {x: all real numbers except 0}
C. {x: all real numbers except –1}
D. {x: all real numbers except 1}
Answer by moshiz08(60) About Me  (Show Source):
You can put this solution on YOUR website!
I know you had other questions, but can you please repost them separately as they belong in different subject areas? Sorry about the trouble.
So we have f%28x%29+=+x%2F%28x+%2B+1%29+
Let's try to find f(1). So we plug in 1 for x to get +f%281%29+=+1%2F%281%2B1%29+=+1%2F2. So 1 is in the domain.
Let's try to find f(0). So we plug in 1 for x to get +f%280%29+=+1%2F%280%2B1%29+=+1%2F1+=+1. So 0 is in the domain.
Let's try to find f(-1). So we plug in -1 for x to get +f%28-1%29+=+1%2F%28-1%2B1%29+=+1%2F0+=+undefined. So -1 cannot be in the domain, because we cannot divide by 0.
Thus, the answer is C: all real numbers except for -1.

The general procedure to finding domain of a rational function is to set the DENOMINATOR equal to ZERO. Since we know that division by zero is not allowed, this will tell us the values at which the function is not defined. In this example, we have (x+1) in the denominator. Setting this equal to zero gives x%2B1+=+0 which is true when x=-1. So we know that x=-1 makes the denominator equal to zero, and thus makes the function undefined, so -1 cannot be in the domain. Thus the domain is the set of real numbers except for -1. I hope this makes sense. Please do repost the other questions for us to take a look at.
CCAAD.