The problem you provided in the image asks us to find the value of $g(-3)$, given the following functions and composition:

1. $f(x) = 2x - 1$
2. $(f \circ g)(x) = -14x + 21$

To solve for $g(-3)$, follow these steps:

Step 1: Understand the composition of functions.

The notation $(f \circ g)(x)$ means $f(g(x))$, which implies that the function $g(x)$ is substituted into the function $f(x)$.

We are given: $f(g(x)) = -14x + 21$ This tells us that applying $f(x) = 2x - 1$ to $g(x)$ will result in $-14x + 21$.

Step 2: Set up the equation using the definition of $f(x)$.

Since $f(x) = 2x - 1$, substitute $g(x)$ into $f(x)$: $f(g(x)) = 2g(x) - 1$ Equate this to the given expression for $(f \circ g)(x)$: $2g(x) - 1 = -14x + 21$

Step 3: Solve for $g(x)$.

Now, solve the equation $2g(x) - 1 = -14x + 21$ for $g(x)$:

1. Add 1 to both sides: $2g(x) = -14x + 22$

2. Divide by 2: $g(x) = -7x + 11$

Step 4: Find $g(-3)$.

Substitute $x = -3$ into the expression for $g(x)$: $g(-3) = -7(-3) + 11 = 21 + 11 = 32$

Thus, the value of $g(-3)$ is $\boxed{32}$.

Would you like more details or further clarification?

Here are some related questions you can explore:

1. How do you find the composition of two functions?
2. What does the notation $f \circ g$ mean in terms of function operations?
3. How do you derive a function when given its composition?
4. What is the significance of function compositions in calculus?
5. How can function composition be applied in real-world scenarios?

Tip: When solving problems with function compositions, always carefully substitute one function into another to avoid errors!