how do you find the domain? Explain?

Question

log(x+7)

log(6) (49-x^2)

squareroot of (x+7)/ (X+2)(x+8)

Answer 1

By definition of logarithms: Positive numbers has logarithm , but negative numbers do not have logarithm.
Then
1) Log (X+7)
X+7>0 or X>-7
===> Domain X is in (-7,+infinity)

2) Log(6) (49-X^2) = Log(6) + Log (49-X^2)
49-X^2>0 or 49>X^2
===>
Domain X is in (-7,+7)

3) square root of (x+7)/ (X+2)(x+8)
By definition of square root:
(X+7)/ (X+2)(X+8)>=0
Also
(X+2)(X+8) different 0, X different -2 and -8
We use critic points Analise and we have make:
===>
Domain X is in (-8,-7] and (-2,+infinity)
X=-7 is included
********************************************

Answer 2

The domain of an expression is the largest set of numbers for which the expression has an acceptable or defined value.

log(x) is defined for all positive real numbers.

log(x + 7) is defined when x + 7 is a positive real number.
x + 7 > 0
x > -7

So, x > -7 is the domain of log(x + 7).

The base six logarithm of 49 - x^2 is defined when 49 - x^2 is positive.

49 - x^2 > 0
multiply both sides by -1
x^2 - 49 < 0
(x + 7)(x -7) < 0 is true when x is between -7 and 7
-7 < x < 7

So, the domain of log(base 6)(49 - x^2) is -7 < x < 7.

sqrt(x) is defined for all nonnegative real numbers.
sqrt(x) is defined for all real numbers greater than or equal to zero.
sqrt(x) is undefined for all negative real numbers.

To determine the domain of sqrt[ (x + 7) / ((x + 2)(x + 8)) ] find values of x where x + 7, x + 2, and x + 8 are zero: -7, -2, and -8.

The sqrt[ (x + 7) / ((x + 2)(x + 8)) ] is undefined at x = -2 and -8, since the denominator is equal to zero at those values. Remember, division by zero is undefined.

The sqrt[ (x + 7) / ((x + 2)(x + 8)) ] is equal to zero at x = -7.

The numbers -8, -7, and -2, divide the real number into four intervals. Choose any number in each interval and check the sign value of each factor to determine if sqrt[ (x + 7) / ((x + 2)(x + 8)) ] is defined or undefined.

x < -8, sqrt[ (-) / ((-)(-)) ] is undefined

-8 < x < -7, sqrt[ (-) / ((-)(+)) ] is defined

-7 < x < -2, sqrt[ (+) / ((-)(+)) ] is undefined

x > -2, sqrt[ (+) / ((+)(+)) ] is defined

So, the domain of sqrt[ (x + 7) / ((x + 2)(x + 8)) ] is values of x between -8 (not included) and -7 (included) and x greater than -2. That is, the domain is all real numbers x where -8 < x < -7 or x = -7 or x > -2.

Answer 3

log(x+7)
The log is undefined for x=<0
So Domain is -7
log(6) (49-x^2)
x can be any real value. the above is a parabola which is continuous over all the real numbers

square root ((x+7)/[(x+2)(x+8)])

x> -2 and -8 The expression is undefined at x = - 8 and -7, but it is defined between these two numbers.

The expression is imaginary if -7

Answer 4

Hello,

1) x > -7 log cannot be negative or 0

2) -7
3) x > -2 or -8
Hope this helps!!

Answer 5

log(x+7), x +7 > 0 ----> x > - 7
S = (-7, +00)

log(6) (49 - x²) -----> 49 - x² > 0

remembering
49 - x² > 0 ---> 49 > x² ---> √49 > √x² ---> | x | < 7
| x | < 7 ---> - 7 < x < 7
S = (- 7, 7)


√[(x+7)/ (x+2)(x+8)]

[(x+7)/ (x² + 10x +16)] >= 0
S = (- 8, -7] or (2, +00)

I wait to have helped.

Answer 6

1) x > -7, logs must be positive

2) -7 < x < 7, logs positive

3) x > -7, sq rt positive, x can not equal -2, (and -8); denominator can not be zero