Domanda del libro di testo
Complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. x² + y²+3x+5y+9/4=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 64
Let f(x) = 2x - 5 g(x) = 4x - 1 h(x) = x² + x + 2. Evaluate the indicated function without finding an equation for the function. f(g[h (1)])
Guida verificata passo dopo passo1
First, identify the innermost function to evaluate, which is \( h(1) \). Substitute \( x = 1 \) into \( h(x) = x^2 + x + 2 \) to find \( h(1) \).
Next, take the result from \( h(1) \) and substitute it into \( g(x) = 4x - 1 \) to find \( g(h(1)) \).
Then, take the result from \( g(h(1)) \) and substitute it into \( f(x) = 2x - 5 \) to find \( f(g(h(1))) \).
Remember to perform each substitution step carefully, simplifying the expressions at each stage before moving to the next function.
By following these steps, you will evaluate \( f(g(h(1))) \) without needing to find the composite function's explicit formula.
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Function Composition
Function composition involves applying one function to the result of another, denoted as (f ∘ g)(x) = f(g(x)). In this problem, you evaluate functions inside out, starting with the innermost function h(1), then applying g to that result, and finally f to the output of g.
Video consigliato:
4:56
Function Composition
Evaluating Functions at a Given Input
Evaluating a function means substituting a specific value for the variable and simplifying. For example, to find h(1), replace x with 1 in h(x) = x² + x + 2 and calculate the result. This step-by-step substitution is essential for nested function evaluation.
Video consigliato:
4:26Evaluating Composed Functions
Order of Operations in Nested Functions
When dealing with nested functions like f(g(h(1))), you must follow the order from the innermost function outward. First evaluate h(1), then use that result as input for g, and finally apply f to the output of g. This ensures accurate and systematic calculation.
Video consigliato:
7:24Multiplying & Dividing Functions
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In Exercises 64–66, begin by graphing the square root function, f(x) = √x. Then use transformations of this graph to graph the given function. g(x) = √(x + 3)
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