The image provides two functions:

$f(x) = 4x - 14$ $g(x) = x^2 - 4x - 3$

We are asked to find $f(g(x))$, which is the composition of the functions $f$ and $g$. This means we will substitute $g(x)$ into $f(x)$.

Steps to find $f(g(x))$:

1. Start by substituting $g(x) = x^2 - 4x - 3$ into $f(x) = 4x - 14$.

   So, $f(g(x)) = f(x^2 - 4x - 3)$.

2. Apply the function $f$ to $g(x)$:

   $f(g(x)) = 4(x^2 - 4x - 3) - 14$

3. Now, distribute the 4 inside the parentheses:

   $f(g(x)) = 4x^2 - 16x - 12 - 14$

4. Combine like terms:

   $f(g(x)) = 4x^2 - 16x - 26$

So, the composition $f(g(x))$ is:

$f(g(x)) = 4x^2 - 16x - 26$

Would you like further details or clarifications on any part of this solution?

Related Questions:

1. What is the composition $g(f(x))$ using the same functions?
2. How would you solve $f(g(x)) = 0$?
3. Can you find the inverse of $f(x)$ or $g(x)$?
4. What are the roots of $g(x) = 0$?
5. What does the graph of $f(g(x))$ look like?

Tip:

When composing functions, make sure to replace the entire input variable in the outer function with the inner function's expression.