Posted by Frank on Sunday, May 2, 2010 at 11:42pm.
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.
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.
Related Questions
MAth - how do i find the domain and range of equations? example: f(x)=ab.solute ...
math - how do i find the domain and range of equations? example: f(x)=ab.solute ...
Math (pre-calculus) - Hey! I have a domain and range question! I don't ...
Calc - Find the functions a) f o g, b) g o f, c) f o f, d) g o g, and their ...
Calculus - Find the functions a) f o g, b) g o f, c) f o f, d) g o g, and their ...
Help! Math (pre-calculus) - Oy! I don't understand this! How do you ...
precalculus check immediately - suppoe f is a function with domain [1,3]and ...
Maths - How to find a range (not domain) of function f(x)=square root of x^2-1/...
algebra - 1.)correct 2.)wrong---> the first term is wrong 4(3a^2)^2 = 36a...
Domain and Range! - What is the domain of the function f(x)=11/Square root of 4-...
For Further Reading
