Domanda del libro di testo
Graph each linear function. 6x-5f(x) - 20 = 0
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Ch. 2 - Functions and Graphs
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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TOC.tableOfContents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Capitolo 3, Problema 83
Find f + g, f - g, fg, and f/g. f(x) = x2 + x + 1, g(x) = x2 -1
Guida verificata passo dopo passo1
Identify the given functions: \(f(x) = x^2 + x + 1\) and \(g(x) = x^2 - 1\).
To find \(f + g\), add the two functions by combining like terms: write \(f(x) + g(x) = (x^2 + x + 1) + (x^2 - 1)\).
To find \(f - g\), subtract \(g(x)\) from \(f(x)\) by combining like terms: write \(f(x) - g(x) = (x^2 + x + 1) - (x^2 - 1)\).
To find the product \(fg\), multiply the two functions: write \(f(x) \cdot g(x) = (x^2 + x + 1)(x^2 - 1)\) and use the distributive property (FOIL) to expand.
To find the quotient \(\frac{f}{g}\), write \(\frac{f(x)}{g(x)} = \frac{x^2 + x + 1}{x^2 - 1}\) and note the domain restriction where \(g(x) \neq 0\) (i.e., \(x^2 - 1 \neq 0\)).
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Function Operations
Function operations involve combining two functions using addition, subtraction, multiplication, or division. For functions f and g, (f + g)(x) = f(x) + g(x), (f - g)(x) = f(x) - g(x), (fg)(x) = f(x) * g(x), and (f/g)(x) = f(x) / g(x), where g(x) ≠ 0.
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Percorso guidato
7:24
Multiplying & Dividing Functions
Polynomial Functions
Polynomial functions are expressions involving variables raised to whole-number exponents with coefficients. Here, f(x) and g(x) are quadratic polynomials, which means their operations result in new polynomials formed by combining like terms.
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Percorso guidato
06:04Introduction to Polynomial Functions
Domain Restrictions in Function Division
When dividing functions, the domain excludes values where the denominator function equals zero. For f/g, it is essential to find where g(x) = 0 and exclude those x-values to avoid undefined expressions.
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Percorso guidato
3:51Domain Restrictions of Composed Functions
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In Exercises 77–92, use the graph to determine a. the function's domain; b. the function's range; c. the x-intercepts, if any; d. the y-intercept, if any; and e. the missing function values, indicated by question marks, below each graph.
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Domanda del libro di testo
In Exercises 82–84, find f + g, f - g, fg, and f/g. Determine the domain for each function. f(x) = 3x - 1, g(x) = x - 5
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Begin by graphing the absolute value function, f(x) = |x|. Then use transformations of this graph to graph the given function. g(x) = |x|+3
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Begin by graphing the absolute value function, f(x) = |x|. Then use transformations of this graph to graph the given function. g(x) = |x+3|
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Domanda del libro di testo
Use the graphs of f and g to solve Exercises 83–90.
Find (f+g)(−3).
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