Math Problem Statement

Let f(x) = x - 1 and g(x) = x^2 - x. Find and simplify the expression (f + g)(-1).

Solution

The problem asks to find and simplify the expression (f+g)(1)(f + g)(-1), given the following functions:

  • f(x)=x1f(x) = x - 1
  • g(x)=x2xg(x) = x^2 - x

We are tasked to evaluate (f+g)(1)(f + g)(-1).

Steps to solve:

  1. Find f(1)f(-1): f(x)=x1    f(1)=11=2f(x) = x - 1 \implies f(-1) = -1 - 1 = -2

  2. Find g(1)g(-1): g(x)=x2x    g(1)=(1)2(1)=1+1=2g(x) = x^2 - x \implies g(-1) = (-1)^2 - (-1) = 1 + 1 = 2

  3. Sum the results: (f+g)(1)=f(1)+g(1)=2+2=0(f + g)(-1) = f(-1) + g(-1) = -2 + 2 = 0

Thus, (f+g)(1)=0(f + g)(-1) = 0.

Let me know if you'd like more details or have further questions!

Here are five related questions you can try:

  1. What is (fg)(1)(f \cdot g)(-1) for the same functions?
  2. Evaluate (f+g)(0)(f + g)(0) for the given functions.
  3. How would you simplify (fg)(1)(f - g)(1)?
  4. What is the derivative of f(x)+g(x)f(x) + g(x)?
  5. Evaluate (fg)(2)(f \cdot g)(2) and simplify.

Tip: Always remember to substitute correctly and carefully simplify when adding functions.

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Math Problem Analysis

Mathematical Concepts

Algebra
Function Addition
Simplification

Formulas

f(x) + g(x) = (f + g)(x)
f(x) = x - 1
g(x) = x^2 - x

Theorems

Basic Function Addition
Evaluation of Functions

Suitable Grade Level

Grade 9-10