Question

Given g of x equals cube root of the quantity x minus 3, on what interval is the function positive?

Answer 1

The interval which the function is positive is (3, ∝)

How to determine the positive interval?

The equation of the function is given as:

g(x) =∛x - 3

Set the radical greater than 0

x - 3 > 0

Add 3 to both sides of the inequality

x > 3

Express as an interval notation

(3, ∝)

Hence, the interval which the function is positive is (3, ∝)

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Answer 2

The function is positive when x is larger than 3, then the interval in where the function is positive is: (3, ∞)

on what interval is the function positive?

The function is positive when g(x) > 0.

Then we need to solve:

∛(x - 3) > 0

We can directly remove the cubic root, because it does not affect the sign of the argument, then:

x - 3 > 0

x > 3

The function is positive when x is larger than 3, then the interval in where the function is positive is: (3, ∞)

If you want to learn more about functions:

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