Answer:
AI-generated answer
To find the value of f(g(x)) = 4 |-3x^2 - 7 - 2| + 3, we need to follow these steps:
1. Start by evaluating the expression inside the absolute value brackets: |-3x^2 - 7 - 2|.
2. Simplify the expression inside the absolute value: -3x^2 - 7 - 2 = -3x^2 - 9.
3. Take the absolute value of the simplified expression: |-3x^2 - 9|.
4. Simplify the absolute value expression: |-3x^2 - 9| = 3x^2 + 9.
5. Substitute the simplified absolute value expression back into the original expression: f(g(x)) = 4(3x^2 + 9) + 3.
6. Simplify further: f(g(x)) = 12x^2 + 36 + 3.
7. Combine like terms: f(g(x)) = 12x^2 + 39.
Therefore, the value of f(g(x)) is 12x^2 + 39.
Explanation: