Explain how to solve the following problems step by step, and reason it should be solved that way:
1) Find domain for each problem and explain in brief in each case. How do you find the domain of these problems without using a graph (don't state the problem only)? Explain this: why is there a difference between in the domain of an even and an odd indexed radical? Why the domain of a function with a square root in the denominator IS different than the domain of a function with square root NOT in the denominator?
A rational function of the form
Is defined for every x except Q(x)=0. (denominator equal to zero)
So find x which corresponding to Q(x)=0. Then domain is all real number except this number.
A square root funtion
Is defined for every x except p(x) <0
So p(x) should be greater than or equal to 0.
Find x to which p(x)> 0 . This is domain.
Here Q(x) is x2+7 .
This is not possible for any real number . So domain is entire real number .
Here Q(x) is x2-3x-18
For a quadratic equation ax2+bx+c=0
Here a=1 ,b= -3 ,c= -18
So domain is all number except x=6 and x= -3
Domain of a cube root funtion is all x .
So domain of
Is all x.
This is rational function with square root funtion.
For square root funtion p(x)= 7-2x
P(x) should be greater than or equal to zero.
Add 2x at both side . This will not effect the inequality.
Divide both side by 2
3.5 ≥ x
So domain is all x less than 3.5 , including 3.5
Now consider condition for rational funtion.
So funtion is defined for every x except
So funtion is not defined at x=3.5
So combining this two domain is all x less than 3.5
Domain of odd indexed radicle is all x.
Domain of even indexed radicle is only posative number.
(-1)2= 12 =1
For odd indexed
They are different.