Math Problem Statement

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

Solution

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

Step 1: Find f(0)f(0)

Given f(x)=2x+5f(x) = 2x + 5, substitute x=0x = 0 into the equation: f(0)=2(0)+5=5f(0) = 2(0) + 5 = 5

Step 2: Find g(f(0))=g(5)g(f(0)) = g(5)

Now, substitute f(0)=5f(0) = 5 into g(x)g(x), which is given as g(x)=x2g(x) = x^2: g(5)=52=25g(5) = 5^2 = 25

Final Answer:

(gf)(0)=25(g \circ f)(0) = 25

Would you like further details or clarification on this?

Here are 5 related questions:

  1. What is (fg)(0)(f \circ g)(0)?
  2. How would you find (gf)(x)(g \circ f)(x) for any xx?
  3. Can you explain the difference between function composition and multiplication?
  4. What is (gf)(2)(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!

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Math Problem Analysis

Mathematical Concepts

Function Composition
Linear Functions
Quadratic Functions

Formulas

f(x) = 2x + 5
g(x) = x^2
(g ∘ f)(x) = g(f(x))

Theorems

Composition of Functions

Suitable Grade Level

Grades 9-10