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

Question

anonymous · Answer

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

perl · Answer

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

imqwerty · Answer

R-{1/7}

theeric · Answer

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 $x>0$.