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use the graph of y = f(x) to graph each function g.
g(x) = f(x-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 19
Find the domain of each function. f(x) = 1/√(x - 3)
Guida verificata passo dopo passo1
Identify the expression inside the square root in the denominator: \(\sqrt{\\(x - 3\")}\). Since the square root is in the denominator, the expression inside the root must be strictly greater than zero to avoid division by zero and undefined values.
Set up the inequality for the radicand (the expression inside the square root): \(x - 3 > 0\).
Solve the inequality for \(x\): add 3 to both sides to get \(x > 3\).
Interpret the solution: the domain of the function consists of all real numbers greater than 3, because for these values the denominator is defined and not zero.
Express the domain in interval notation: \((3, \infty)\).
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Domain of a Function
The domain of a function is the set of all possible input values (x-values) for which the function is defined. For rational and root functions, the domain is restricted by values that cause division by zero or taking the square root of a negative number.
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3:51
Domain Restrictions of Composed Functions
Square Root Function Restrictions
A square root function requires the radicand (expression inside the root) to be greater than or equal to zero to produce real number outputs. For f(x) = 1/√(x - 3), the expression x - 3 must be strictly greater than zero because the root is in the denominator.
Video consigliato:
02:20Imaginary Roots with the Square Root Property
Division by Zero
Division by zero is undefined in mathematics. Since the square root is in the denominator, the radicand cannot be zero because that would make the denominator zero, causing the function to be undefined at that point.
Video consigliato:
03:42Finding Zeros & Their Multiplicity
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