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March 30, 2017

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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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