https://file.aiquickdraw.com/mathbot/file/1725552533387m2li9maj.jpg

The question in the image asks to find \( f(g(x)) \), where:

- \( f(x) = 3x - 5 \)
- \( g(x) = 2x - 1 \)

To find \( f(g(x)) \), we substitute \( g(x) \) into \( f(x) \).

### Step-by-Step Solution:

1. \( f(g(x)) = f(2x - 1) \)
   
   Since \( f(x) = 3x - 5 \), replace \( x \) in \( f(x) \) with \( g(x) = 2x - 1 \):

2. \( f(g(x)) = 3(2x - 1) - 5 \)

3. Simplify:

   \[
   f(g(x)) = 6x - 3 - 5
   \]
   \[
   f(g(x)) = 6x - 8
   \]

Thus, \( f(g(x)) = 6x - 8 \).

Would you like further clarification, or any additional details on this solution? Here are some related questions:

1. What is the process to find \( g(f(x)) \)?
2. How does composition of functions work generally?
3. Can you explain how domain and range are affected by function composition?
4. How would you invert \( f(x) \) or \( g(x) \) from this problem?
5. What would happen if \( g(x) \) was a quadratic function instead?

**Tip**: In function composition, always substitute the inner function into the outer function carefully, and simplify step by step!

Find f(g(x)) where f(x) = 3x - 5 and g(x) = 2x - 1.

Learn how to find the composition of two functions, f(x) = 3x - 5 and g(x) = 2x - 1, and calculate f(g(x)). This step-by-step solution explains function composition in algebra, suitable for high school students.

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