The image contains the following mathematical functions and tasks:

Functions:

1. $a(x) = -3x + 5$
2. $b(x) = 11x - 1$
3. $c(x) = -8x - 3$

Tasks:

The tasks require evaluating specific expressions involving these functions.

Problems:

1. $(a - c)^{-1}(1)$
2. $(a + c)^{-1}(0)$
3. $(a - (c + b)^2)^{-1}(-1)$

These involve subtracting or adding the functions $a(x)$, $b(x)$, and $c(x)$, and then finding the inverse of the resulting expression evaluated at a specific value.

Let's break down the tasks:

1. For $(a - c)^{-1}(1)$:

   • First, compute $a(x) - c(x)$.
   • Then, find the inverse of the resulting function.
   • Finally, evaluate the inverse at $x = 1$.

2. For $(a + c)^{-1}(0)$:

   • First, compute $a(x) + c(x)$.
   • Then, find the inverse of the resulting function.
   • Finally, evaluate the inverse at $x = 0$.

3. For $(a - (c + b)^2)^{-1}(-1)$:

   • First, compute $c(x) + b(x)$, square the result.
   • Subtract this from $a(x)$.
   • Then, find the inverse of the resulting function.
   • Finally, evaluate the inverse at $x = -1$.

Would you like me to walk you through the steps to solve each of these problems in detail?

Related Questions:

1. What does it mean for a function to have an inverse?
2. How do you compute the inverse of a linear function?
3. What operations are necessary to simplify expressions like $a(x) - c(x)$?
4. How do you handle squared terms like $(c + b)^2$ when combining functions?
5. How do we evaluate a function's inverse at a particular value?

Tip:

When finding the inverse of a linear function, remember that the inverse function essentially "undoes" the original operation by switching $x$ and $y$, then solving for $y$.