Final answer:
The value of x when g(x) = 24 for the function g(x) = x^3 - 3 is 3, since adding 3 to both sides of the equation allows us to take the cube root of 27 to find x.
Step-by-step explanation:
The student is asking to find the value of x when g(x) = 24 for the function g(x) = x^3 - 3. To solve for x, the equation should be set equal to 24: x^3 - 3 = 24. The next step is to isolate the x^3 term by adding 3 to both sides of the equation, resulting in x^3 = 27. Since the cube root of 27 is 3, we find that x = 3.
To find the value of x when g(x) = 24, we will substitute 24 for g(x) in the equation g(x) = x^3 - 3 and solve for x.
24 = x^3 - 3
Adding 3 to both sides, we get:
27 = x^3
To solve for x, we can take the cube root of both sides:
x = ∛27
Since the cube root of 27 is 3, the value of x is 3.