Let 
f
(
x
)
=
x
2
+
3
x
+
7
. Evaluate and simplify by multiplying, distributing and collecting like terms when applicable. f(x/2)=

Given the function \( f(x) = x^2 + 3x + 7 \), we are tasked with finding \( f\left(\frac{x}{2}\right) \).

### Step-by-step process:

1. **Substitute \( \frac{x}{2} \) into the function**:
   \[
   f\left(\frac{x}{2}\right) = \left(\frac{x}{2}\right)^2 + 3\left(\frac{x}{2}\right) + 7
   \]

2. **Simplify each term**:
   - \( \left(\frac{x}{2}\right)^2 = \frac{x^2}{4} \)
   - \( 3\left(\frac{x}{2}\right) = \frac{3x}{2} \)

   So the expression becomes:
   \[
   f\left(\frac{x}{2}\right) = \frac{x^2}{4} + \frac{3x}{2} + 7
   \]

3. **Combine the terms**:
   \[
   f\left(\frac{x}{2}\right) = \frac{x^2}{4} + \frac{3x}{2} + 7
   \]
   This is the simplified form of \( f\left(\frac{x}{2}\right) \).

Would you like any further details or explanations on this?

Here are 5 follow-up questions:
1. What is the value of \( f\left(\frac{x}{2}\right) \) when \( x = 4 \)?
2. How does changing the coefficient of \( x^2 \) in \( f(x) \) affect the function?
3. Can you rewrite the expression \( f\left(\frac{x}{2}\right) \) in terms of a common denominator?
4. What happens if you apply this method to other functions, such as \( g(x) = x^3 - 2x + 5 \)?
5. What is the domain of the function \( f(x) = x^2 + 3x + 7 \)?

**Tip**: Always pay attention to distributing correctly when substituting variables in functions, as it's easy to miss details!

Let f(x) = x^2 + 3x + 7. Evaluate and simplify by multiplying, distributing and collecting like terms when applicable. f(x/2) =

Learn how to substitute and simplify the function f(x) = x^2 + 3x + 7 for f(x/2) with a step-by-step solution. This problem explores key algebraic concepts such as function substitution and simplifying expressions. Suitable for Grades 8-10 students.

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