Posted by Frank on Sunday, May 2, 2010 at 11:42pm.
1.) Find the domain and range for:
f(x)= 4x20/ the square root of 36x^2
2.) Solve the equation:
log6 (x11) + log6 (x6) = 2
3.) Solve the inequality:
x^2  2x  3 is greater than 0

Math SAT Sheet  Reiny, Monday, May 3, 2010 at 12:22am
1. remember that the denominator √(36  x^2) cannot be zero or negative,
so shouldn't 6 < x < +6 ??
2. log6 [(x11)(x6)] = 2
(x11)(x6) = 6^2
x^2  17x + 66 = 36
x^2  17x + 30 = 0
(x15)(x2) = 0
x = 15 or x = 2
A lot of students would stop here and think they have the right answer, but remember that we can only take logs of positive numbers, so looking at our original we can see clearly that x > 11
so x = 15 is the only answer.

Math SAT Sheet  Reiny, Monday, May 3, 2010 at 12:26am
3. x^2  2x  3 > 0
(x3)(x+1) > 0
"critical" values are x = 3 and x = 1
try a number < 1, say x = 5
statement: (8)(4) > 0 ? YES
try a number between 1 and 3, say x = 0
statement: (3)(1) > 0 False!
try a number > 3, say x = 5
statement: (2)(6)>0 YES
so x < 1 OR x > 3, x any real number.
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