Explanation? for these SAT Math problems?

<ol>
<li><p>f(x)=(x+1)^3/4
For the function f , defined above, what are all values of x for which f(x) is a real number?
answer: x is greater than or equal to -1</p></li>
<li><p>There are g gallons of paint available to paint a house. After n gallons have been used, then, in terms of g and n, what percent of the has not been used?
answer: 100(g-n) / g %</p></li>
<li><p>If x is an integer and 2<x<7, how many different triangles are there with sides of lengths 2,7, and x?
answer: one</p></li>
<li><p>If a>b and a(b-a)=0, which of the following must be true?
I. a=0
II.b<0
III.a-b>0
answer: I, II, and III</p></li>
<li><pre><code> y | _______
| /
|/
(-2,0) /|
----------------------
o |\
| \
| _______
</code></pre></li>
</ol>

<p>The graph above is a parabola that is symmetric about the x axis. Which of the following could be an equation of the parabola?
answer: x=y^2 - 2</p>

<p>4.</p>

<p>I. The only way for a(b-a)=0 is to have a = 0. True.
II. You know a>b, and because a=0, B has to be less than 0. True.
III. 0-(any negative number) is positive. Thus, it has to be greater than 0. True.</p>

<ol>
<li>Triangle inequality rule. x=6 is the only value for x that works in the triangle inequality rule and the definition of the problem for x, which means there is one possible triangle.</li>
</ol>

<p>Is 1 really a SAT Reasoning problem? It expects knowledge of complex numbers. In any case rewrite it as sqrt(x+1)*sqrt(sqrt(x+1)). Assume x is real (not part of the problem statement). So sqrt(x+1) is a real number when x+1 is real, or when x (assumed to be a real number) is greater than -1.</p>

<p>For #2 you just simply employ the percent change formula. The difference/ original, or in this case (g-n)/g, and you multiply it by 100 to get the actual percent.</p>

<p>(1) Since we’re taking an even root (4th root), we must have x+1 greater than or equal to 0. Add -1 to both sides of the inequality to get x greater than or equal to -1.</p>

<p>(2) I believe this is actually a multiple choice question. In my opinion, the best and safest way to do this one is by “picking numbers.” Since it’s a percent problem, let g = 100. Let’s also let n = 25. Then 75 percent has not been used. Now just plug in g and n into each answer choice and eliminate any that do not yield 75.</p>

<p>Important remark: If the question is multiple choice you should really give us the choices. There are many SAT strategies that take advantage of the fact that there are only 5 possible answers.</p>