Domain of a Function Part 2

[marshall1432]

What is the domain of the function f(x) = 2x/(x2 + 1)? Give your answer in interval notation, using INF for infinity.

My solution:

(x2+1)=0
(x+1)(x+1)=0
-1,-1

(-INF,-1) U (-1,INF)

Did I set that one up right and work it right? thanks

 

[jacket81]

First, x^2+1 is not equal to (x + 1)(x + 1). Second:

x^2 + 1 = 0

x^2 = -1

You can't solve this, since x^2 can't be -1.

The domain of f(x) = 2x / (x^2 + 1) has to be real numbers. The numerator can be zero, but you can't divide by zero. So you have to check for any x-value where the denominator might be zero. But x^2 + 1 is never zero. The domain is "all reals".

 

[marshall1432]

so then the answer is just x?

 

[Mrspi]

As has been explained, x can be ANY real number. So, the domain is

x is an element of (-inf, +inf)