Domanda del libro di testo
Evaluate each function at the given values of the independent variable and simplify. h(x) = x4 - x2 +1 b. h (-1)
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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 31b
Find f−g and determine the domain for each function. f(x) = 2x + 3, g(x) = x − 1
Guida verificata passo dopo passo1
Identify the given functions: \(f(x) = 2x + 3\) and \(g(x) = x - 1\).
Find the difference of the functions, which is \(f - g\). This means subtract \(g(x)\) from \(f(x)\): write the expression \(f(x) - g(x)\).
Substitute the given functions into the expression: \(f(x) - g(x) = (2x + 3) - (x - 1)\).
Simplify the expression by distributing the negative sign and combining like terms: \(2x + 3 - x + 1\).
Determine the domain of \(f - g\). Since both \(f(x)\) and \(g(x)\) are linear functions defined for all real numbers, the domain of \(f - g\) is all real numbers.
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Function Subtraction (f - g)
Function subtraction involves creating a new function by subtracting the output of one function from another for the same input value. For functions f(x) and g(x), (f - g)(x) = f(x) - g(x). This operation combines the two functions into one, which can then be analyzed or simplified.
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Adding & Subtracting Functions
Domain of a Function
The domain of a function is the set of all input values (x-values) for which the function is defined. When combining functions, the domain of the resulting function is the intersection of the domains of the original functions, ensuring all operations are valid for those inputs.
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3:51Domain Restrictions of Composed Functions
Linear Functions
Linear functions are polynomial functions of degree one, typically written as f(x) = mx + b, where m and b are constants. They have a constant rate of change and their graphs are straight lines. Understanding their properties helps in performing operations like addition or subtraction and determining domains.
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06:07Linear Inequalities
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