Posted by **Frank** on Sunday, May 2, 2010 at 11:42pm.

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 -
**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 [(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 -
**Reiny**, Monday, May 3, 2010 at 12:26am
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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