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f(x) = x - 3, g(x) = x² Find (f + g)(x). 2 - (f + g)(x) = x+x-3 Find the domain of (f + g)(x). (Enter your answer using interval notation.) -∞0,00 Find (f - g)(x). (f - g)(x) = Find the domain of (f – g)(x). (Enter your answer using interval notation.) L Find (fg)(x). (fg)(x) Find the domain of (fg)(x). (Enter your answer using interval notation.) ind (x). (-0 = Find the domain of (x). (Enter your answer using interval notation.)

f(x) = x - 3, g(x) = x² Find (f + g)(x). 2 - (f + g)(x) = x+x-3 Find the domain of (f + g)(x). (Enter your answer using interval notation.) -∞0,00 Find (f - g)(x). (f - g)(x) = Find the domain of (f – g)(x). (Enter your answer using interval notation.) L Find (fg)(x). (fg)(x) Find the domain of (fg)(x). (Enter your answer using interval notation.) ind (x). (-0 = Find the domain of (x). (Enter your answer using interval notation.)

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter3: Functions
Section3.4: Operations On Functions
Problem 124E
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Consider the following functions
### Functions and Their Operations Given the functions \( f(x) = x - 3 \) and \( g(x) = x^2 \). #### Problem 1: Addition of Functions **Find \((f + g)(x)\):** \[ (f + g)(x) = f(x) + g(x) = (x - 3) + x^2 \] \[ = x^2 + x - 3 \] - The answer is correctly boxed: \[ \boxed{x^2 + x - 3} \] **Find the domain of \((f + g)(x)\). (Enter your answer using interval notation.)** - The answer is: \[ \boxed{(-\infty, \infty)} \] However, it is marked incorrect with a red X. #### Problem 2: Subtraction of Functions **Find \((f - g)(x)\):** \[ (f - g)(x) = f(x) - g(x) = (x - 3) - x^2 \] \[ = -x^2 + x - 3 \] **Find the domain of \((f - g)(x)\). (Enter your answer using interval notation.)** - The answer is: \[ \boxed{(-\infty, \infty)} \] #### Problem 3: Multiplication of Functions **Find \((fg)(x)\):** \[ (fg)(x) = f(x) \cdot g(x) = (x - 3) \cdot x^2 \] \[ = x^3 - 3x^2 \] **Find the domain of \((fg)(x)\). (Enter your answer using interval notation.)** - The answer is: \[ \boxed{(-\infty, \infty)} \] #### Problem 4: Division of Functions **Find \((\frac{f}{g})(x)\):** \[ \left( \frac{f}{g} \right)(x) = \frac{f(x)}{g(x)} = \frac{x-3}{x^2} \] \[ \boxed{\frac{x-3}{x^2}} \] This boxed expression is marked incorrect with a red X. **Find the domain of \( \left( \frac{f}{g} \right)(x) \). (Enter your answer using interval
Transcribed Image Text:### Functions and Their Operations Given the functions \( f(x) = x - 3 \) and \( g(x) = x^2 \). #### Problem 1: Addition of Functions **Find \((f + g)(x)\):** \[ (f + g)(x) = f(x) + g(x) = (x - 3) + x^2 \] \[ = x^2 + x - 3 \] - The answer is correctly boxed: \[ \boxed{x^2 + x - 3} \] **Find the domain of \((f + g)(x)\). (Enter your answer using interval notation.)** - The answer is: \[ \boxed{(-\infty, \infty)} \] However, it is marked incorrect with a red X. #### Problem 2: Subtraction of Functions **Find \((f - g)(x)\):** \[ (f - g)(x) = f(x) - g(x) = (x - 3) - x^2 \] \[ = -x^2 + x - 3 \] **Find the domain of \((f - g)(x)\). (Enter your answer using interval notation.)** - The answer is: \[ \boxed{(-\infty, \infty)} \] #### Problem 3: Multiplication of Functions **Find \((fg)(x)\):** \[ (fg)(x) = f(x) \cdot g(x) = (x - 3) \cdot x^2 \] \[ = x^3 - 3x^2 \] **Find the domain of \((fg)(x)\). (Enter your answer using interval notation.)** - The answer is: \[ \boxed{(-\infty, \infty)} \] #### Problem 4: Division of Functions **Find \((\frac{f}{g})(x)\):** \[ \left( \frac{f}{g} \right)(x) = \frac{f(x)}{g(x)} = \frac{x-3}{x^2} \] \[ \boxed{\frac{x-3}{x^2}} \] This boxed expression is marked incorrect with a red X. **Find the domain of \( \left( \frac{f}{g} \right)(x) \). (Enter your answer using interval
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