교과서 질문
Composite functions
Let ƒ(x) = x³, g (x) = sin x and h(x) = √x .
Evaluate h(g( π/2)).
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Ch. 1 - Functions
Briggs3rd EditionCalculus: Early TranscendentalsISBN: 9780136847243
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TOC.tableOfContents
- Ch. 1 - Functions210
- Ch. 2 - Limits371
- Ch. 3 - Derivatives633
- Ch. 4 - Applications of the Derivative412
- Ch. 5 - Integration328
- Ch. 6 - Applications of Integration331
- Ch. 7 - Logarithmic, Exponential Functions, and Hyperbolic Functions177
- Ch. 8 - Integration Techniques394
- Ch. 9 - Differential Equations179
- Ch. 10 - Sequences and Infinite Series339
- Ch. 11 - Power Series218
- Ch.12 - Parametric and Polar Curves215
1장, 문제 19b
Composite functions
Let ƒ(x) = x³, g (x) = sin x and h(x) = √x .
Find h (ƒ (x)).
검증된 단계별 안내1
Step 1: Understand the problem. We are asked to find the composite function h(ƒ(x)), which means we need to substitute ƒ(x) into h(x).
Step 2: Identify the given functions. We have ƒ(x) = x^3 and h(x) = \(\sqrt{x}\).
Step 3: Substitute ƒ(x) into h(x). This means replacing the x in h(x) with ƒ(x).
Step 4: Write the expression for the composite function. h(ƒ(x)) becomes h(x^3).
Step 5: Simplify the expression. Since h(x) = \(\sqrt{x}\), h(x^3) becomes \(\sqrt{x^3}\).
비슷한 문제에 대한 검증된 영상 답변:
이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
영상 길이:
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주요 개념
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Composite Functions
A composite function is formed when one function is applied to the result of another function. It is denoted as (f ∘ g)(x) = f(g(x)). Understanding how to combine functions is essential for evaluating expressions like h(f(x)), where the output of f(x) becomes the input for h.
추천 영상:
3:48
Evaluate Composite Functions - Special Cases
Function Notation
Function notation is a way to represent functions and their operations clearly. For example, f(x) represents the output of function f when x is the input. Recognizing how to read and interpret function notation is crucial for correctly applying functions in composite scenarios.
추천 영상:
가이드 코스
7:24Multiplying & Dividing Functions
Basic Functions and Their Properties
Familiarity with basic functions, such as polynomial functions (like f(x) = x³), trigonometric functions (like g(x) = sin x), and radical functions (like h(x) = √x), is vital. Each function has unique properties that affect how they interact in compositions, influencing the overall behavior of the composite function.
추천 영상:
가이드 코스
06:21Properties of Functions
관련 실천
교과서 질문
Evaluating trigonometric functions Without using a calculator, evaluate the following expressions or state that the quantity is undefined.
cos (2π/3)
267
views
교과서 질문
Composite functions
Let ƒ(x) = x³, g (x) = sin x and h(x) = √x.
Find the domain of g o ƒ.
355
views
교과서 질문
Composite functions
Let ƒ(x) = x³, g (x) = sin x and h(x) = √x.
Find ƒ(g(h( x))).
363
views
교과서 질문
Yeast growth Consider a colony of yeast cells that has the shape of a cylinder. As the number of yeast cells increases, the cross-sectional area A (in mm²) of the colony increases but the height of the colony remains constant. If the colony starts from a single cell, the number of yeast cells (in millions) is approximated by the linear function N(A) - CₛA, where the constant Cₛ is known as the cell-surface coefficient. Use the given information to determine the cell-surface coefficient for each of the following colonies of yeast cells, and find the number of yeast cells in the colony when the cross-sectional area A reaches 150 mm². (Source: Letters in Applied Microbiology, 594, 59, 2014)
The scientific name of baker’s or brewer’s yeast (used in making bread, wine, and beer) is Saccharomyces cerevisiae. When the cross-sectional area of a colony of this yeast reaches 100 mm², there are 571 million yeast cells.
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