Determine the domain

Question

Determine the domain of the functions show work

 

a) f(x)= 1/x^3

 

b) f(x)= (x+4)^2/4x-3

 

c) f(x)= x^2+3x-10/x^2=2x

Answer 1

Remember the rule that "Thou Shalt Not Divide by Zero" - hence any value of x that results in the denominator being equal to zero, must be excluded from the domain:

 

a) f(x)=1/x³  has denominator x³ - hence we want that:

 

     x³≠0

      x≠0   (taking the cube root of both sides)

 

Hence the domain is {x|x ≠0}, or in interval notation (-infinity, 0) ∪ (0, infinity)

 

 

b) f(x)=(x+4)²/(4x-3)  has denominator 4x-3 - hence we want that:

 

    4x-3≠0  

    4x≠3     (adding 3 to both sides)

      x≠3/4  (dividing both sides by 4)

 

hence the domain is {x|x≠3/4}, or in interval notation (-infinity, 3/4) ∪ (3/4, infinity)

 

 

c) f(x)=(x²+3x-10)/(x²-2x) (first factor the numerator and denominator)

     

        =(x+5)(x-2)/x(x-2)   (now reduce common factors to one through division)

 

        = (x+5)/x   this has denominator x - hence we want that:

 

 

  x≠0

 

therefore the domain is {x|x≠0}, or in interval notation (-infinity,0) ∪ (0, infinity)