교과서 질문
Where do inverses exist? Use analytical and/or graphical methods to determine the largest possible sets of points on which the following functions have an inverse.
ƒ(x) = |2x + 1|
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Ch. 1 - Functions
Briggs3rd EditionCalculus: Early TranscendentalsISBN: 9780136847243
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Table of contents
- 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 1.60
Solving equations Solve the following equations.
5(ˣ³) = 29
검증된 단계별 안내1
Step 1: Start by isolating the term with the variable. Divide both sides of the equation by 5 to get x^3 = \(\frac{29}{5}\).
Step 2: To solve for x, take the cube root of both sides of the equation. This will give you x = \(\sqrt\)[3]{\(\frac{29}{5}\)}.
Step 3: Simplify the expression if possible. In this case, \(\sqrt\)[3]{\(\frac{29}{5}\)} is already in its simplest form.
Step 4: Consider the properties of cube roots. Remember that the cube root of a number can be positive or negative, but since we are dealing with real numbers, we focus on the principal (positive) root.
Step 5: Verify your solution by substituting x back into the original equation to ensure that both sides are equal.
비슷한 문제에 대한 검증된 영상 답변:
이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
영상 길이:
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주요 개념
질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.
Exponential Equations
Exponential equations involve variables in the exponent, such as the equation 5(x³) = 29. To solve these equations, one typically isolates the exponential term and applies logarithmic functions to both sides, allowing for the extraction of the variable from the exponent.
추천 영상:
5:47
Solving Exponential Equations Using Logs
Logarithms
Logarithms are the inverse operations of exponentiation. They allow us to solve for the exponent in an equation. For example, if we have an equation in the form a^b = c, we can use logarithms to express b as log_a(c), which is essential for solving exponential equations.
추천 영상:
7:30Logarithms Introduction
Algebraic Manipulation
Algebraic manipulation involves rearranging and simplifying equations to isolate the variable of interest. This includes operations such as addition, subtraction, multiplication, and division, as well as applying properties of equality to maintain balance in the equation while solving for the unknown.
추천 영상:
05:25Determine Continuity Algebraically
관련 실천
교과서 질문
For a certain constant a>1, ln a≈3.8067 . Find approximate values of log₂ a and logₐ 2 using the fact that ln 2≈0.6931.
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교과서 질문
Missing piece Let g(x) = x² + 3 Find a function ƒ that produces the given composition.
(g o ƒ ) (x) = x⁴ + 3
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교과서 질문
Use the graph of ƒ to find ƒ⁻¹ (2),ƒ⁻¹ (9), and ƒ⁻¹ (12) <IMAGE>
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교과서 질문
Graph the following functions.
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교과서 질문
Solving equations Solve each equation.
sin² 2Θ = 1/2, -π/2 ≤ Θ ≤ π/2
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