Find (f o g)(x) from f(x)= 3x and g(x)=4x²-5x+1

To find \((f \circ g)(x)\), we need to evaluate \(f(g(x))\), which means substituting \(g(x)\) into the function \(f(x)\).

Given:
- \(f(x) = 3x\)
- \(g(x) = 4x^2 - 5x + 1\)

### Steps:
1. Start with the expression for \(f(x)\):  
   \(f(x) = 3x\)
   
2. Now, substitute \(g(x)\) into \(f(x)\):  
   \[
   f(g(x)) = 3(g(x)) = 3(4x^2 - 5x + 1)
   \]
   
3. Distribute the 3 to each term inside the parentheses:
   \[
   f(g(x)) = 3(4x^2) + 3(-5x) + 3(1)
   \]
   \[
   f(g(x)) = 12x^2 - 15x + 3
   \]

So, \((f \circ g)(x) = 12x^2 - 15x + 3\).

Would you like further details or clarification on any part?

Here are 5 related questions:
1. How do you find \((g \circ f)(x)\) with these functions?
2. What happens if you swap the order of composition in functions?
3. Can you differentiate \((f \circ g)(x)\)?
4. What are the domains of \(f(x)\), \(g(x)\), and \((f \circ g)(x)\)?
5. How do you determine whether a composition of functions is one-to-one?

**Tip**: Always make sure to substitute the entire function when performing composition, including all terms.

Learn how to find the composition of two functions, f(x) = 3x and g(x) = 4x² - 5x + 1. This problem explores key algebraic concepts such as function composition and quadratic functions. Detailed step-by-step solution provided. Suitable for Grades 9-12.

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