Question 19

Explanation

We are given the functions $f(x) = 2x - 3$ and $g(x) = x^2 + 4x - 1$. We need to find the value of $a + b + c$ from the composite function $(g \circ f)(x) = ax^2 + bx + c$.

First, let's determine the composite function $(g \circ f)(x)$:

Expand the squared term and the product:

Combine like terms:

From the form $ax^2 + bx + c$, we obtain:

So the value of $a + b + c$ is:

Thus, the value of $a + b + c = -4$.