Find the domain of the function. h(x) = x-2/x^3 - 49x

Question

h(x)=x-2 over x to the 3rd-49x. Find the domain. 

Answer 1

I BET THAT YOU INTEND THIS TO BE A RATIONAL ALGEBRAIC FUNCTION having numerator x-2 and

denominator x(x-7)(x+7).  YOU MUST WRITE PARENTHESES TO MAKE THIS PERFECTLY CLEAR.

 

Answer: the domain is all reals except 0, -7  and 7.

Answer 2

h(x) = (x-2)/(x³-49x)

 

Domain = {x l x³ - 49x ≠ 0}

 

            = {x l x(x² - 49)≠0}

 

            = {x l x(x+7)(x-7) ≠ 0}

 

            = {x l x ≠ 0, 7, -7}

 

            = (-∞, -7) ∪ (-7,0) ∪ (0,7) ∪ (7,∞)