given f(x)=x2 and g(x)=4x , find (f o g) (x) simplify



Given the functions \( f(x) = x^2 \) and \( g(x) = 4x \), we are tasked with finding \( (f \circ g)(x) \), which represents the composition of the functions \( f \) and \( g \).

### Step 1: Define the composition
The composition \( (f \circ g)(x) \) means that we first apply \( g(x) \) and then apply \( f \) to the result. Symbolically, this can be written as:
\[
(f \circ g)(x) = f(g(x))
\]

### Step 2: Substitute \( g(x) \) into \( f(x) \)
Since \( g(x) = 4x \), we substitute \( 4x \) into the expression for \( f(x) = x^2 \):
\[
(f \circ g)(x) = f(4x) = (4x)^2
\]

### Step 3: Simplify the expression
Now, simplify \( (4x)^2 \):
\[
(4x)^2 = 16x^2
\]

### Final Answer:
\[
(f \circ g)(x) = 16x^2
\]

Would you like any further details or clarification on this? Here are five related questions for deeper exploration:

1. What is the domain of \( (f \circ g)(x) \)?
2. How would you find \( (g \circ f)(x) \)?
3. What happens if \( f(x) \) is a different function, say \( f(x) = x^3 \)?
4. How can you graph the composition of two functions like \( f(x) \) and \( g(x) \)?
5. Can you generalize the process of composing two arbitrary functions?

**Tip:** Always remember to perform the function on the *inside* of the composition first and simplify step by step.

given f(x)=x^2 and g(x)=4x, find (f o g)(x) simplify

Discover how to find and simplify the composition of two functions, f(x)=x^2 and g(x)=4x. This detailed explanation covers the algebraic steps involved in calculating (f o g)(x), leading to a simplified result of 16x^2. Ideal for Grades 9-10 students learning function compositions and quadratic functions.

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