given f(x)=2x+5 and g(x)=x^2 find (g of f)(0)

To find \((g \circ f)(0)\), also known as \(g(f(0))\), we will first find \(f(0)\) and then substitute the result into \(g(x)\).

### Step 1: Find \(f(0)\)
Given \(f(x) = 2x + 5\), substitute \(x = 0\) into the equation:
\[
f(0) = 2(0) + 5 = 5
\]

### Step 2: Find \(g(f(0)) = g(5)\)
Now, substitute \(f(0) = 5\) into \(g(x)\), which is given as \(g(x) = x^2\):
\[
g(5) = 5^2 = 25
\]

### Final Answer:
\[
(g \circ f)(0) = 25
\]

Would you like further details or clarification on this?

Here are 5 related questions:
1. What is \( (f \circ g)(0) \)?
2. How would you find \( (g \circ f)(x) \) for any \(x\)?
3. Can you explain the difference between function composition and multiplication?
4. What is \( (g \circ f)(2) \)?
5. How do you find the inverse of a function?

**Tip:** Always double-check the order of composition when working with multiple functions—it's crucial for getting the right result!

Given f(x) = 2x + 5 and g(x) = x^2, find (g of f)(0).

Learn how to find (g of f)(0) when f(x) = 2x + 5 and g(x) = x^2 with a detailed step-by-step solution. This problem involves function composition, including linear and quadratic functions, and is suitable for students in Grades 9-10.

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