Question

Domain of
a) x^20
b) 1/(x-3)
c)1/(4x^2-21x-18)
d) sqrt(4x^2-21x-18)
e) 1/ sqrt(4x^2-21x-18)

Answer 1

Domain

a. x^20. All real values of x.

b. 1/(x-3).
3 is not in the domain, because it gives a denominator of 0. So the domain is all real values of x except 3:
3 > x >3.

c. 1 / (4x^2-21x-18) =
1 / (x-6)(4x+3) .
Domain: All real values of x except 6:
6 > x > 6.

d. sqrt(4x^2-21x-18) =
sqrt((x-6)(4x+3)).

Domain: All real values of x that are
=> 6. Values below 6 will result in a
negative value under the radical.

Domain: X => 6.

e. 1 / sqrt(4x^2-21x-18) =
1 / sqrt((x-6)(4x+3)).
6 is not in the domain,because it gives a denominator of 0. Values below 6 results in a negative value under the radical. Therefore, all values greater than 6 are in the domain:

Domain: X > 6.

Answer 2

1. sqrt x^2-5x-14
2. cube root x-6/sqrt x^2-x-30
3. y= ln2x-12