Division of a real analytic function

**Nagual** · March 9th 2011, 10:45 AM

Can anybody can help me?

On some interval [a,b] suppose that I have a real analytic function f and a real contiuous function g, where g is different from zero in [a,b]. Does f/g will be real analytic on [a,b]? Otherwise what can I say on the function f/g ?

**TheEmptySet** · March 9th 2011, 10:58 AM

What if $g(x)$ is the piecewise linear function that takes values

$\displaystyle g(a)=1, g\left( \frac{a+b}{2}\right)=2,g(b)=1$

is the function

$\displaystyle h(x)=\frac{f(x)}{g(x)}$ analytic?

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