<PRE><B>Question 82645</B>
&lt;b&gt;First question:&lt;/b&gt; You are correct. The function is neither even or odd. there are many functions like this. For example f(x)=x-1.&lt;br /&gt;

There are many ways to construct such functions. Any odd function plus a (non-zero) constant will be neither odd or even. Can you explain why?&lt;br /&gt;

In fact an even function plus and odd function will be neither even or odd (apart from one special case) can you think what this case is?&lt;br /&gt;

&lt;b&gt;Second question:&lt;/b&gt; I don&#39;t understand the notation you&#39;re using. I haven&#39;t done this kind of maths in years. Do you mean:&lt;br /&gt;

*[tex \frac{x-3}{\sqrt{x+4}}]&lt;br /&gt;

Well, the answer depends on what sets we&#39;re working with, but I&#39;m gonna guess that you&#39;re working with real numbers.&lt;br /&gt;

The way I would tackle a question like this, is to go through these steps:&lt;br /&gt;

1) Identify which operations you are doing which can make things go bad.&lt;br /&gt;

2) For each operation that can go bad, work out at which points it goes bad.&lt;br /&gt;

3) Take these bad points out of *[tex \mathbb{R}](The real numbers *[tex (-\infty,\infty)]), and that leaves you the domain.&lt;br /&gt;

Well, the (possibly) bad operations you have here are the division and the square root.&lt;br /&gt;

The division will go bad if we divide by zero, so that&#39;s when x=-4. The square root will go bad if the inside is negative, and that&#39;s when *[tex x\lt -4].&lt;br /&gt;

So the bad points are when *[tex x\leq -4]. Taking this away from *[tex \mathbb{R}] leaves the domain as:&lt;br /&gt;

*[tex x\in(-4, \infty)]&lt;br /&gt;

Note: this isn&#39;t one of the choices you&#39;ve been given. It is open on the left, whereas the choice was closed on the left.&lt;br /&gt;

Hope that helps,
Kev</PRE>