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
