The domain of the function is {x| x≠±5, x≠ 0} which is the correct answer would be option (A)
What are the domain and range of the function?
The domain of the function includes all possible x values of a function, and the range includes all possible y values of the function.
Given the function as
[tex]h(x) = \dfrac{3x}{x(x^2-25)}[/tex]
Set the denominator [tex]h(x) = \dfrac{3x}{x(x^2-25)}[/tex] equal to 0 to determine where the expression is undefined.
⇒ x(x²−25)=0
⇒ x = 0, -5, 5
All real numbers except for 0, -5, and 5
Since there can't be a zero in the denominator, the equation can't have the solutions 0, -5, and 5.
Interval notation of the domain as
⇒ (-∞, -5) ∪ (-5, 0) u (0, 5) ∪ (5, ∞)
Set-builder notation as
⇒ {x| x≠±5, x≠ 0} or
⇒ {x| x≠ 0, 5, -5}
Hence, the domain of the function is {x| x≠±5, x≠ 0} which is the correct answer would be option (A)
Learn more about the domain and the range here:
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