Domain Solver

Tuesday, July 15th, 2008 at 11:59 pm

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Domain Solver

Trig help...?

Solver for exact values.
A.) (x+2)/(((2x-7)(x+4)(x+6))) ≥ 0

B.) x +√ (x-3) =15

Compute the domain for the function.
C.) f(x) = √ (x^2 - 3x +2) / (x-6)

please please help me...I would be very helpful if you showed and explained the steps...thanks so much.

A)
That nasty thing equals 0 or null set (undefined) whenever one or more of the factors equals 0. Between these four points, the equation is either positive or negative. So, you need to test to see whether the equation is + or - at 5 points. I hope this isn't completely foreign to you, cause if it is, your math teacher really is crazy to assign this.
First, solve for the zeros or undefineds:
x + 2 = 0
x = -2 (Zero)

2x - 7 = 0
x = 3.5 (Undefined)

x + 4 = 0
x = -4 (Undefined)

x + 6 = 0
x = -6 (Undefined)

So, in order, the zeros/undefineds are -6. -4, -2, and 3.5.
Plot on number line:
<-------------------------------->
. . . . -6. . -4. . -2. . 0. . . . . 3.5
Look back at the actual equation now.
When x is less than -6 (try -8 to see it), the equation is positive.
When -6 < x < -4, the equation is negative (try -5 for an example).
When -4 < x < -2, the equation is positive again.
-2 < x < 3.5, the equation is negative.
Finally, x > 3.5, the equation is positive.
Notice that the pattern is + - + -, like it often is.
You want the values of x that make the equation positive or 0, so x<-6 OR -4 > x >= -2 OR x > 3.5 is the answer.