Question

Find the domain of h(x)= 1/ 3x^2-15x

Answer 1

Hello!

To find the domain of the function h(x), we need to find the values of x where it is undefined.

We can begin by factoring the denominator of the rational function, h(x).

h(x) = 1/(3x² - 15x) (factor 3x from the binomial)

h(x) = 1/3x(x - 5)

After factoring the denominator, apply the zero product property.

3x = 0 (divide both sides by 3)

x = 0

x - 5 = 0 (add 5 to both sides)

x = 5

The values of 0 and 5 cause h(x) to be undefined. The function h(x) comes from negative infinity to zero, where there is an asymptote. Also, from zero to five, there is also an asymptote. Finally, the function h(x) also goes to infinity from five.  

So therefore, the domain of the function h(x) is: (-∞, 0) ∪ (0, 5) ∪ (5, ∞).

Answer 2

Question:

Find the domain of h(x) = 1/3x^2 - 5x

So, the domain of a function is the set of values for which the function is defined.

Answer:

Domain = (-∞, ∞)

The domain is a negative infinity and a positive infinity because its gonna keep going down and keep going up. So a negative infinity is less than a positive infinity so it would be

(-∞ < x < ∞)

Hope that helped!

~Serina