Math Problem Statement

Given f(x) = x + 1 and g(x) = x², what is (g ∘ f)(x)?

Solution

To solve the problem from the uploaded image:

Problem:

We are given two functions:

  1. f(x)=x+1f(x) = x + 1
  2. g(x)=x2g(x) = x^2

We need to determine (gf)(x)(g \circ f)(x), which represents the composition g(f(x))g(f(x)).

Steps to Solve:

  1. Start with f(x)=x+1f(x) = x + 1.
    Substituting f(x)f(x) into g(x)g(x), we have:
    g(f(x))=g(x+1)g(f(x)) = g(x + 1)

  2. Since g(x)=x2g(x) = x^2, replacing xx with x+1x + 1 gives:
    [ g(x + 1) = (x + 1)^2 \

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Math Problem Analysis

Mathematical Concepts

Function Composition
Quadratic Functions

Formulas

g(f(x)) = g(x + 1)
g(x) = x²

Theorems

Basic Function Composition Rules

Suitable Grade Level

Grades 9-10