text: # Math SAT Sheet
  
  posted by .
  
  1.) Find the domain and range for:
  
  f(x)= 4x-20/ the square root of 36-x^2
  
  2.) Solve the equation:
  
  log6 (x-11) + log6 (x-6) = 2
  
  3.) Solve the inequality:
  
  x^2 - 2x - 3 is greater than 0
  
  • Math SAT Sheet -
  
  1. remember that the denominator √(36 - x^2) cannot be zero or negative,
  so shouldn't -6 < x < +6 ??
  
  2. log6 [(x-11)(x-6)] = 2
  (x-11)(x-6) = 6^2
  x^2 - 17x + 66 = 36
  x^2 - 17x + 30 = 0
  (x-15)(x-2) = 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 -
  
  3. x^2 - 2x - 3 > 0
  (x-3)(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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