The domain of f/g
consists of numbers x for which g(x) cannot equal 0 that are in the domains of
both f and g.
Let’s take this equation as an example:
If f(x) = 3x - 5 and g(x)
= square root of x-5, what is the domain of (f/g)x.
For x to be in the domain of (f/g)(x), it must be
in the domain of f and in the domain of g since (f/g)(x) = f(x)/g(x). We also
need to ensure that g(x) is not zero since f(x) is divided by g(x). Therefore,
there are 3 conditions.
x must be in the domain of f:
f(x) = 3x -5 are in the domain of x and all real numbers x.
x must be in the domain of g:
g(x) = √(x - 5) so x - 5 ≥ 0 so x ≥ 5.
g(x) can not be 0: g(x)
= √(x - 5) and √(x - 5) = 0 gives x = 5 so x ≠ 5.
Hence to x x ≥ 5 and x ≠ 5
so the domain of (f/g)(x) is all x satisfying x > 5.
Thus, satisfying <span>satisfy all
three conditions, x x ≥ 5 and x ≠ 5 so the domain of (f/g)(x) is all x
satisfying x > 5.</span>
Answer:
The equation is always false
Step-by-step explanation:
X2 - 25 = 0
Add 25 on each side.
x2 = 25
Divide by 2 on each side.
x = 12.5
Answer:
Reflection over the x- axis
Step-by-step explanation:
Answer: The numerator and denominator degrees of freedom (respectively) for the critical value of F are <u>4</u> and<u> 118 .</u>
Step-by-step explanation:
We know that , for critical value of F, degrees of freedom for numerator = k-1
and for denominator = n-k, where n= Total observations and k = number of independent variables.
Here, Numbers of independent variables(k) = 5
Total observations (n)= 123
So, Degrees of freedom for numerator = 5-1=4
Degrees of freedom for denominator =123-5= 118
Hence, the numerator and denominator degrees of freedom (respectively) for the critical value of F are <u>4</u> and<u> 118 .</u>
