Given the functions
f
and
g
below, find
f
(
g
(
−
2
)
)
.
f
(
x
)
=
−
3
x
+
1
g
(
x
)
=
−
4
x
−
3

To find \( f(g(-2)) \), we need to follow these steps:

1. **First, find \( g(-2) \)**:
   \[
   g(x) = -4x - 3
   \]
   Substitute \( x = -2 \) into the function \( g(x) \):
   \[
   g(-2) = -4(-2) - 3
   \]
   \[
   g(-2) = 8 - 3 = 5
   \]

2. **Next, find \( f(g(-2)) = f(5) \)**:
   \[
   f(x) = -3x + 1
   \]
   Substitute \( x = 5 \) into the function \( f(x) \):
   \[
   f(5) = -3(5) + 1
   \]
   \[
   f(5) = -15 + 1 = -14
   \]

So, \( f(g(-2)) = -14 \).

Would you like more details on the steps involved, or do you have any other questions? Here are some related questions you might find interesting:

1. What is \( g(f(-2)) \)?
2. What are the roots of the function \( f(x) = -3x + 1 \)?
3. If \( g(x) \) were quadratic, how would that affect the calculation?
4. How would the composition change if \( g(x) = -4x^2 - 3 \)?
5. What is the general formula for \( f(g(x)) \) based on the given functions?

**Tip:** Always start by working with the inner function when dealing with compositions of functions.

Learn how to compute f(g(-2)) using the linear functions f(x) = -3x + 1 and g(x) = -4x - 3. Step-by-step solution provided. Suitable for high school students.

Math Problem Statement

Given the functions f and g below, find f ( g ( − 2 ) ) . f ( x )

− 3 x + 1 g ( x )

Solution

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