Posted by **John** on Sunday, September 26, 2010 at 6:19pm.

What is the domain of (sec(x)-1)/(x^2)?

- Math -
**MathMate**, Sunday, September 26, 2010 at 8:25pm
The domain of a function

f(x)=g(x)/h(x) is given by

dom(g(x))∩dom(h(x))\{x|h(x)=0}

which means to find the domain of f(x), we calculate the intersection of the domains of g(x) and h(x), *less* the points at which h(x)=0 (vertical asymptotes).

In your case,

dom(sec(x)-1) is ℝ,

dom(x²) is also ℝ

All you need to do is to find

dom(sec(x)-1) ∩ dom(x²) but exclude points at which x²=0.

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