Find the Domain for each function

Question

a) g(x)= x/(x^2-1)

 

b) h(x)= (3x-12)^1/2

Answer 1

a)

 

Solve the equation 

x² - 1 = 0

 

The value of x is your restriction.  All other values of x are your domain.

 

b)

 

Solve the inequality 

3x - 12 ≥ 0

 

The value of x is your domain.

Answer 2

a) g(x)= x/(x^2-1)

 

set denominator = 0

 

x²-1 =0
(x+1)(x-1) =0

x=-1 and x=+1

 

domain is all real number except x=1,-1

 

{x | x ≠ 1,x≠-1}

 

______________________________________________________

 

b) h(x)= (3x-12)^1/2

 

h(x) =√ (3x-12)

 

so

 

(3x-12) >= 0

3x >= 12

x >= 4

 

 

[4,+infinity]