Math Problem Statement

If f(x) = x^2 + 3x and g(x) = 1, then what is g ∘ f(x) equal to?

Solution

To analyze the problem and provide the solution:

The question involves the functions f(x)=x2+3xf(x) = x^2 + 3x and g(x)=1g(x) = 1, and asks for the composition gf(x)g \circ f(x). Let me clarify the steps:

  1. Composition definition: (gf)(x)=g(f(x))(g \circ f)(x) = g(f(x)), so we evaluate gg at f(x)f(x).
  2. Since g(x)=1g(x) = 1 for any xx, regardless of the input f(x)f(x), the value of g(f(x))g(f(x)) is always 11.
  3. Therefore, gf(x)=1g \circ f(x) = 1.

The correct answer is 1 (A).

Let me know if you want further details or have questions! Here are 5 related questions:

  1. How does function composition work in other examples?
  2. Why does g(x)=1g(x) = 1 result in a constant output for the composition?
  3. What happens when the order of composition is reversed?
  4. What are common applications of function composition in mathematics?
  5. How do we verify compositions graphically?

Tip: Always simplify the inner function first in a composition to reduce complexity.

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Math Problem Analysis

Mathematical Concepts

Function Composition
Constant Functions
Algebra

Formulas

(g ∘ f)(x) = g(f(x))
f(x) = x^2 + 3x
g(x) = 1

Theorems

Function Composition Rule

Suitable Grade Level

Grades 9-11