## anonymous one year ago Find the domain of the function f(x)= x^2/(7x-1) and leave your answer in set notation.

1. anonymous

$f(x)=\frac{ x ^{2} }{ 7x-1 }$

2. perl

The domain is the set of all real number inputs that make sense. Does it make sense to divide by zero?

3. imqwerty

R-{1/7}

4. theEric

I agree with @perl. The thing is, ALL functions have domains - that is a required for a function to be a function. Just, it's $$\it{assumed}$$ a lot of the time. So, when no one tells you what it is, you have to assume that your $$x$$ can be any value that gives you a result in the "range." That is the range part of the domain and range that are needed for the function. Normally, we make another assumption - the range is real numbers only (no $$\sqrt{-1}$$, for sure). So, the result of the function needs a value! Some expressions are undefined, like $$\dfrac{\text{anything}}0$$. So, if some value would make $$f(x)$$ be $$\dfrac{\text{anything}}0$$, then $$x$$ is NOT that. In other problems, you might see something like $$g(x)=\sqrt x$$. If $$x$$ is negative, like $$\sqrt{-4}$$, the result is not real, and we don't want it. There, we say $$x$$ is NOT negative, so $$x>0$$.