Math Problem Statement

Jika f(x) = 2x - 1 dan (f ∘ g)(x) = -14x + 21, nilai dari g(-3) = ....

Solution

The problem in the image asks to solve for g(3)g(-3) given the following:

  1. f(x)=2x1f(x) = 2x - 1
  2. (fg)(x)=14x+21(f \circ g)(x) = -14x + 21, which means f(g(x))=14x+21f(g(x)) = -14x + 21.

Steps:

  1. From f(g(x))=14x+21f(g(x)) = -14x + 21, we know that applying the function f(x)=2x1f(x) = 2x - 1 to g(x)g(x) must give the expression on the right side. f(g(x))=2g(x)1=14x+21f(g(x)) = 2g(x) - 1 = -14x + 21

  2. Solve for ( g(x) \

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Math Problem Analysis

Mathematical Concepts

Function Composition
Algebra

Formulas

f(g(x)) = -14x + 21
f(x) = 2x - 1

Theorems

Composition of Functions

Suitable Grade Level

Grades 10-12