Question

Determine g(3x²) for the following function. g(x)=-6x²+3x+3

Answer 1

To determine g(3x²) for the given function g(x) = -6x² + 3x + 3, substitute 3x² for x, and simplify to get g(3x²) = -54x´ + 9x² + 3.

Step-by-step explanation:

To determine g(3x²) for the function g(x) = -6x² + 3x + 3, we simply substitute 3x² for every occurrence of x in the function.

Step-by-Step Solution:

1. Start with the given function g(x) = -6x² + 3x + 3.
2. Replace every x with 3x² to get g(3x²) = -6(3x²)² + 3(3x²) + 3.
3. Simplify the equation:
   g(3x²) = -6(9x´) + 9x² + 3.
4. Combine like terms: g(3x²) = -54x´ + 9x² + 3.

Therefore, the final expression for g(3x²) is -54x´ + 9x² + 3.