f(x) = 4x + 3 and q(x) - 2 - 3x

find (f•g)(3)

To solve \((f \circ g)(3)\), we need to evaluate the composition of two functions \(f(x)\) and \(g(x)\) at \(x = 3\). However, you've provided the function \(f(x) = 4x + 3\) and a partial expression \(q(x) - 2 - 3x\) which seems like an incomplete or typo for the second function.

Let me assume you meant \(g(x) = 2 - 3x\) as the second function. If this is the correct interpretation, we'll proceed as follows:

### Step-by-step Solution:

1. **Define the functions:**

   \[
   f(x) = 4x + 3
   \]
   \[
   g(x) = 2 - 3x
   \]

2. **Find \(g(3)\):**

   Substitute \(x = 3\) into \(g(x)\):
   \[
   g(3) = 2 - 3(3)
   \]
   \[
   g(3) = 2 - 9
   \]
   \[
   g(3) = -7
   \]

3. **Find \((f \circ g)(3)\):**

   \((f \circ g)(3) = f(g(3))\). We already know \(g(3) = -7\).

   Now, substitute \(g(3) = -7\) into \(f(x)\):
   \[
   f(g(3)) = f(-7)
   \]
   \[
   f(-7) = 4(-7) + 3
   \]
   \[
   f(-7) = -28 + 3
   \]
   \[
   f(-7) = -25
   \]

### Conclusion:

\[
(f \circ g)(3) = -25
\]

Would you like more details or have any questions about this solution?

### Related Questions:

1. What is \((g \circ f)(3)\) given the functions above?
2. How do you find the inverse of \(f(x) = 4x + 3\)?
3. What is the domain and range of \(f(x)\) and \(g(x)\)?
4. How would you graph the functions \(f(x)\) and \(g(x)\)?
5. What is the result of \((f \circ f)(x)\) for any \(x\)?

### Tip:

When solving function compositions, always evaluate the inner function first, then use its result to compute the outer function.

Learn how to evaluate the function composition (f ∘ g)(3) where f(x) = 4x + 3 and g(x) = 2 - 3x. Follow a detailed step-by-step solution with explanations and calculations.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation