To find \( g(f(-1)) \), we'll follow these steps:

1. **Find \( f(-1) \):**
   Given \( f(x) = 4x + 3 \), substitute \( x = -1 \) into \( f(x) \):
   \[
   f(-1) = 4(-1) + 3 = -4 + 3 = -1
   \]
   So, \( f(-1) = -1 \).

2. **Find \( g(f(-1)) = g(-1) \):**
   Now, using \( g(x) = x - 2 \), substitute \( x = -1 \) into \( g(x) \):
   \[
   g(-1) = -1 - 2 = -3
   \]

Thus, \( g(f(-1)) = -3 \).

Would you like more details or have any questions?

Here are 5 related questions:
1. What is \( g(f(x)) \) in terms of \( x \)?
2. Find \( f(g(2)) \) given the same functions.
3. If \( f(x) = 4x + 3 \) and \( g(x) = x^2 - 2 \), what is \( g(f(1)) \)?
4. Find \( g(f(x)) \) when \( f(x) = 2x + 1 \) and \( g(x) = 3x - 5 \).
5. What is the inverse function of \( f(x) = 4x + 3 \)?

**Tip:** In composite functions, always work from the innermost function to the outermost function.

f(x) = 4x + 3, g(x) = x - 2. Find g(f(-1))

Explore how to solve the composite function g(f(-1)) for the functions f(x) = 4x + 3 and g(x) = x - 2. This detailed step-by-step guide helps students in Grades 9-10 understand function composition and basic algebraic operations.

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