Question

F(x)=1/x^2 and g(x)= 5/x^2 what is the domain of the functions f and g

Answer 1

Restrictions for f and g:  denominators can't be equal to zero.

                        1 
•  For  f(x)  =  —— :
                        x² 

x² ≠ 0

x ≠ 0


So the domain of f is

Dom(f) = {x ∈ R:  x ≠ 0}

Dom(f) = R*


or using the interval notation,

Dom(f) = ]–∞, 0[ ∪ ]0, +∞[ .

________


                        5 
•  For  g(x)  =  —— :
                        x²


Since g(x) = 5 · f(x), the restrictions for g are the same:

x² ≠ 0

x ≠ 0


So the domain of g is also

Dom(g) = {x ∈ R:  x ≠ 0}

Dom(g) = R*


or using the interval notation,

Dom(g) = ]–∞, 0[ ∪ ]0, +∞[.


I hope this helps. =)


Tags:  function set domain restriction algebra