https://file.aiquickdraw.com/mathbot/file/172670487138733kss5z9.jpg

The problem from the image you uploaded is:

Given \( f(x) = 3x + a \) and \( (f \circ f)(x) = 9x + a + 3 \), you are asked to find the value of \( f(a) \).

Let's break down the problem:

1. \( f(x) = 3x + a \) — This is the original function.
2. \( (f \circ f)(x) \) means applying \( f \) to the result of \( f(x) \). So first, we apply \( f \) to \( x \):
   \[ f(x) = 3x + a \]
   Applying \( f \) again to the result:
   \[ f(f(x)) = f(3x + a) \]
   Substitute \( 3x + a \) into \( f \):
   \[ f(3x + a) = 3(3x + a) + a = 9x + 3a + a \]

We know \( (f \circ f)(x) = 9x + a + 3 \), so:
   \[ 9x + 4a = 9x + a + 3 \]

Equating the coefficients:
   \[ 4a = a + 3 \]
   \[ 3a = 3 \]
   \[ a = 1 \]

Substituting \( a = 1 \) into \( f(x) \):
   \[ f(x) = 3x + 1 \]

Now, we find \( f(a) \):
   \[ f(a) = f(1) = 3(1) + 1 = 4 \]

So, \( f(a) = 4 \).

**Answer: C. 4**

Would you like more details or have any questions about the steps involved? Here are some additional topics you might find interesting:
1. How do function compositions work in general?
2. What happens if the coefficients of \( x \) had been different?
3. How to solve for \( x \) when \( f(x) = g(x) \) for non-linear functions?
4. The concept of function inverses and their properties.
5. How to graph the composition of two functions.

**Tip:** When solving problems involving compositions of functions, always verify your final answers by substituting back into the original equations to ensure consistency.

Diketahui f(x) = 3x + a dan (f o f)(x) = 9x + a + 3, maka nilai f(a) = ...

Learn how to solve a function composition problem where f(x) = 3x + a and (f o f)(x) = 9x + a + 3. This solution involves algebraic manipulation and function application. Suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation