Math Problem Statement

Let f(x) = √(x + 3) and g(x) = x² - x. Find and simplify the expression (f - g)(1).

Solution

We are tasked with finding and simplifying the expression (fg)(1)(f - g)(1), where:

f(x)=x+3andg(x)=x2x.f(x) = \sqrt{x + 3} \quad \text{and} \quad g(x) = x^2 - x.

To calculate (fg)(1)(f - g)(1), we will follow these steps:

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

f(1)=1+3=4=2.f(1) = \sqrt{1 + 3} = \sqrt{4} = 2.

Step 2: Find g(1)g(1)

g(1)=121=11=0.g(1) = 1^2 - 1 = 1 - 1 = 0.

Step 3: Calculate (fg)(1)(f - g)(1)

(fg)(1)=f(1)g(1)=20=2.(f - g)(1) = f(1) - g(1) = 2 - 0 = 2.

Thus, (fg)(1)=2(f - g)(1) = 2.

Would you like further details on the steps, or do you have any questions?


Here are 5 related questions:

  1. How would you calculate (f+g)(1)(f + g)(1) with the same functions?
  2. What is the general formula for (fg)(x)(f - g)(x) for any xx?
  3. How do you solve (fg)(x)=0(f - g)(x) = 0?
  4. Can you find the derivative of f(x)f(x) and g(x)g(x)?
  5. What happens to f(x)f(x) and g(x)g(x) as xx approaches infinity?

Tip: Always substitute the values carefully, especially under the square root, to avoid errors.

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Math Problem Analysis

Mathematical Concepts

Algebra
Function Operations
Square Roots

Formulas

f(x) = √(x + 3)
g(x) = x² - x
(f - g)(x) = f(x) - g(x)

Theorems

Square root simplification
Basic function evaluation

Suitable Grade Level

Grades 9-10