Final answer:
To find (fg)(-2), substitute the expression for g(x) into f(x), simplify the expression, and then substitute x = -2 to evaluate the result.
Step-by-step explanation:
To find (fg)(-2), we need to first evaluate the composition of the two functions. To do this, we substitute the expression for g(x) into f(x), replacing x with 4x - 3:
f(g(x)) = -2(4x - 3)² - 3(4x - 3) - 1
Simplifying this expression gives f(g(x)) = -2(16x² - 24x + 9) - 12x + 9 - 1 = -32x² + 48x - 18 - 12x + 8 = -32x² + 36x - 10
Now, we need to evaluate f(g(-2)), which means we substitute x = -2 into the simplified expression above:
f(g(-2)) = -32(-2)² + 36(-2) - 10 = -32(4) + 36(-2) - 10 = -128 - 72 - 10 = -210