Question

Evaluate the Function g(t) = 3t^3 + 3t^2.

a) g(-4t) = 96t^3 - 48t^2
b) g(-4t) = -96t^3 + 48t^2
c) g(-4t) = -96t^3 - 48t^2
d) g(-4t) = 96t^3 + 48t^2

Answer 1

After substituting -4t for t in the function g(t) = 3t^3 + 3t^2 and simplifying, the correct evaluation of g(-4t) is -96t^3 - 48t^2, which corresponds to option c).

Step-by-step explanation:

To evaluate the function g(t) = 3t^3 + 3t^2 at g(-4t), we need to substitute -4t for every instance of t in the function.

• Replace t with -4t: g(-4t) = 3(-4t)^3 + 3(-4t)^2.
• Cube -4t: (-4t)^3 = -64t^3.
• Square -4t: (-4t)^2 = 16t^2.
• Combine the terms: g(-4t) = 3*(-64t^3) + 3*(16t^2).
• Multiply the coefficients: g(-4t) = -192t^3 + 48t^2.

The correct answer is option c) g(-4t) = -96t^3 - 48t^2, which is the result of the evaluation after combining like terms.