Function Notation
Muhtasari
Mathematics needs a compact, unambiguous way to talk about functions, and that is what function notation provides. The single symbol f(x) packs in the name of the rule, its input, and its output, all at once. Once you are fluent in this shorthand, evaluating, inverting and combining functions becomes clean and quick.
In this lesson you will read and use the notations \(f(x)\) and \(f:x\mapsto\ldots\), evaluate a function at a value, and meet the two operations that build new functions from old: the inverse \(f^{-1}\) and the composite \(fg(x)=f(g(x))\). You will also see what \(f^2(x)\) really means, which is not what many students first guess.
Malengo
- Recognise and use function notation, including f(x), f : x maps to, the inverse f-inverse(x), composite functions fg(x), and f squared (x) meaning f(f(x)).
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Tathmini ya Somo
Hongera kwa kukamilisha somo la Function Notation. Sasa kwa kuwa umechunguza dhana na mawazo muhimu, ni wakati wa kuweka ujuzi wako kwa mtihani. Sehemu hii inatoa mazoezi mbalimbali maswali yaliyoundwa ili kuimarisha uelewaji wako na kukusaidia kupima ufahamu wako wa nyenzo.
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- Given f(x) = 2x + 3, what is f(5)? A. 10 B. 13 C. 16 D. 25 Answer: B
- Given f(x) = 2x + 3, what is f(-1)? A. -1 B. 1 C. 2 D. 5 Answer: B
- What does f^2(x) mean for a function f? A. [f(x)]^2 B. f(f(x)) C. 2 f(x) D. f(x) + f(x) Answer: B
- Given f(x) = 2x + 3 and g(x) = x^2, what is fg(x)? A. (2x + 3)^2 B. 2x^2 + 3 C. 4x + 9 D. 2x + 3 Answer: B
- The inverse of f(x) = 2x + 3 is: A. (x - 3)/2 B. (x + 3)/2 C. 1/(2x + 3) D. 2x - 3 Answer: A
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Vitabu Vinavyopendekezwa
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Sehemu ya kitabu
Composition of Functions
Combine functions using algebraic operations.
"College Algebra: Composition of Functions" by OpenStax, OpenStax, Rice University, licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). Source: https://openstax.org/books/college-algebra/pages/3-4-composition-of-functions. Access for free at https://openstax.org/books/college-algebra/pages/1-introduction
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Sehemu ya kitabu
Inverse Functions
Verify inverse functions.
"College Algebra: Inverse Functions" by OpenStax, OpenStax, Rice University, licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). Source: https://openstax.org/books/college-algebra/pages/3-7-inverse-functions. Access for free at https://openstax.org/books/college-algebra/pages/1-introduction
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