https://file.aiquickdraw.com/mathbot/file/1726256971242nvghif2y.jpg

Let's solve the given function composition problem step by step. The question asks to find \((f \circ g)(4)\), which means you need to evaluate the composition of \( f(x) \) and \( g(x) \) at \( x = 4 \). The given functions are:

\[
f(x) = -3x - 14
\]
\[
g(x) = x^2 - x - 5
\]

### Step 1: Find \( g(4) \)
Substitute \( x = 4 \) into the function \( g(x) \):

\[
g(4) = 4^2 - 4 - 5 = 16 - 4 - 5 = 7
\]

### Step 2: Find \( f(g(4)) = f(7) \)
Now that we know \( g(4) = 7 \), substitute \( 7 \) into \( f(x) \):

\[
f(7) = -3(7) - 14 = -21 - 14 = -35
\]

### Final Answer:
Thus, \((f \circ g)(4) = -35\).

It looks like the previously entered answer of \(-182\) was incorrect, as the correct value should be \(-35\).

Do you want more details or have any questions? Here are some additional related problems you can explore:

1. What is \((g \circ f)(4)\)?
2. How do you find the domain of the composition \( (f \circ g)(x) \)?
3. Can \( f \circ g \) be defined for all real numbers?
4. What happens if \( g(x) \) is a more complex function, such as a rational function?
5. How would the process change if \( f(x) \) or \( g(x) \) were piecewise functions?

**Tip**: When dealing with composition of functions, always evaluate the inside function first and then use its result in the outer function!

Given the definitions of f(x) and g(x) below, find the value of (f ∘ g)(4).

Learn how to solve the function composition problem (f ∘ g)(4), where f(x) = -3x - 14 and g(x) = x^2 - x - 5. This problem involves substituting g(4) into f(x) and calculating the result. Suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation