Explanation Given: f ( z ) = z 3 Key Concept Applied: Function: Function is defined as a rule for a relationship between an input, or independent, quantity and an output, or dependent, quantity in which each input value uniquely determines one output value. We simply say that “the output is a function of the input”. Domain: The set of possible input values to a function. Range: The set of possible output values of a function. Table of Various types of functions, their domain and range Type of Function Mathematical Representation of function Domain Range Graph 1 . Constant function f ( x ) = c All real numbers ( − ∞ , ∞ ) A single real number, c [ c ] Horizontal Line. 2 . Identity function f ( x ) = x All real numbers ( − ∞ , ∞ ) All real numbers ( − ∞ , ∞ ) Line for which each x − coordinates equals the corresponding y − coordinates. 3 . Quadratic (or) Squaring function f ( x ) = x 2 All real numbers ( − ∞ , ∞ ) All nonnegative real numbers [ 0 , ∞ ) U − Shaped curve. It has an intercept at ( 0 , 0 ) 4 . Cubic function f ( x ) = x 3 All real numbers ( − ∞ , ∞ ) All real numbers ( − ∞ , ∞ ) Graph is symmetric with respect to origin. It has an intercept at ( 0 , 0 ) 5 . Reciprocal function f ( x ) = 1 x ( − ∞ , 0 ) ∪ ( 0 , ∞ ) ( − ∞ , 0 ) ∪ ( 0 , ∞ ) No intercepts 6 . Reciprocal squared function f ( x ) = 1 x 2 ( − ∞ , 0 ) ∪ ( 0 , ∞ ) ( 0 , ∞ ) 7 . Square Root function f ( x ) = x 2 All nonnegative real numbers [ 0 , ∞ ) All nonnegative real numbers [ 0 , ∞ ) Graph is increasing on the interval ( 0 , ∞ ) . It has an intercept at ( 0 , 0 ) 8 . Cube Root function f ( x ) = x 3 All real numbers ( − ∞ , ∞ ) All real numbers ( − ∞ , ∞ ) 9 . Absolute value function f ( x ) = | x | All real numbers ( − ∞ , ∞ ) All nonnegative real numbers [ 0 , ∞ ) One-to-One function: A function f is called a one-to-one function f it never takes on the same value twice, that is, f ( x 1 ) ≠ f ( x 2 ) where x 1 ≠ x 2 ...

Loose-leaf Version for Calculus: Early Transcendentals Combo 3e & WebAssign for Calculus: Early Transcendentals 3e (Life of Edition)

3rd Edition

ISBN: 9781319019846

Author: Jon Rogawski, Colin Adams

Publisher: W. H. Freeman

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Question

Chapter 1.5, Problem 14E

To determine

A domain on which $f$ is one-to-one and a formula for the inverse of $f$ restricted to this domain. Sketch the graphs of $f$ and $f^{- 1}$ for the given exercise $f (z) = z^{3}$

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Chapter 1.5, Problem 13E

Chapter 1.5, Problem 15E

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1 pts Let F and G be vector fields such that ▼ × F(0, 0, 0) = (0.76, -9.78, 3.29), G(0, 0, 0) = (−3.99, 6.15, 2.94), and G is irrotational. Then sin(5V (F × G)) at (0, 0, 0) is Question 1 -0.246 0.072 -0.934 0.478 -0.914 -0.855 0.710 0.262 .

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Chapter 1 Solutions

Loose-leaf Version for Calculus: Early Transcendentals Combo 3e & WebAssign for Calculus: Early Transcendentals 3e (Life of Edition)

Ch. 1.1 - Prob. 1PQ Ch. 1.1 - Prob. 2PQ Ch. 1.1 - Prob. 3PQ Ch. 1.1 - Prob. 4PQ Ch. 1.1 - Prob. 5PQ Ch. 1.1 - Prob. 6PQ Ch. 1.1 - Prob. 7PQ Ch. 1.1 - Prob. 8PQ Ch. 1.1 - Prob. 9PQ Ch. 1.1 - Prob. 10PQ

Ch. 1.1 - Prob. 1E Ch. 1.1 - Prob. 2E Ch. 1.1 - Prob. 3E Ch. 1.1 - Prob. 4E Ch. 1.1 - Prob. 5E Ch. 1.1 - Prob. 6E Ch. 1.1 - Prob. 7E Ch. 1.1 - Prob. 8E Ch. 1.1 - Prob. 9E Ch. 1.1 - Prob. 10E Ch. 1.1 - Prob. 11E Ch. 1.1 - Prob. 12E Ch. 1.1 - Prob. 13E Ch. 1.1 - Prob. 14E Ch. 1.1 - Prob. 15E Ch. 1.1 - Prob. 16E Ch. 1.1 - Prob. 17E Ch. 1.1 - Prob. 18E Ch. 1.1 - Prob. 19E Ch. 1.1 - Prob. 20E Ch. 1.1 - Prob. 21E Ch. 1.1 - Prob. 22E Ch. 1.1 - Prob. 23E Ch. 1.1 - Prob. 24E Ch. 1.1 - Prob. 25E Ch. 1.1 - Prob. 26E Ch. 1.1 - Prob. 27E Ch. 1.1 - Prob. 28E Ch. 1.1 - Prob. 29E Ch. 1.1 - Prob. 30E Ch. 1.1 - Prob. 31E Ch. 1.1 - Prob. 32E Ch. 1.1 - Prob. 33E Ch. 1.1 - Prob. 34E Ch. 1.1 - Prob. 35E Ch. 1.1 - Prob. 36E Ch. 1.1 - Prob. 37E Ch. 1.1 - Prob. 38E Ch. 1.1 - Prob. 39E Ch. 1.1 - Prob. 40E Ch. 1.1 - Prob. 41E Ch. 1.1 - Prob. 42E Ch. 1.1 - Prob. 43E Ch. 1.1 - Prob. 44E Ch. 1.1 - Prob. 45E Ch. 1.1 - Prob. 46E Ch. 1.1 - Prob. 47E Ch. 1.1 - Prob. 48E Ch. 1.1 - Prob. 49E Ch. 1.1 - Prob. 50E Ch. 1.1 - 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Prob. 45E Ch. 1.3 - Prob. 46E Ch. 1.3 - Prob. 47E Ch. 1.4 - Prob. 1PQ Ch. 1.4 - Prob. 2PQ Ch. 1.4 - Prob. 3PQ Ch. 1.4 - Prob. 4PQ Ch. 1.4 - Prob. 5PQ Ch. 1.4 - Prob. 6PQ Ch. 1.4 - Prob. 1E Ch. 1.4 - Prob. 2E Ch. 1.4 - Prob. 3E Ch. 1.4 - Prob. 4E Ch. 1.4 - Prob. 5E Ch. 1.4 - Prob. 6E Ch. 1.4 - Prob. 7E Ch. 1.4 - Prob. 8E Ch. 1.4 - Prob. 9E Ch. 1.4 - Prob. 10E Ch. 1.4 - Prob. 11E Ch. 1.4 - Prob. 12E Ch. 1.4 - Prob. 13E Ch. 1.4 - Prob. 14E Ch. 1.4 - Prob. 15E Ch. 1.4 - Prob. 16E Ch. 1.4 - Prob. 17E Ch. 1.4 - Prob. 18E Ch. 1.4 - Prob. 19E Ch. 1.4 - Prob. 20E Ch. 1.4 - Prob. 21E Ch. 1.4 - Prob. 22E Ch. 1.4 - Prob. 23E Ch. 1.4 - Prob. 24E Ch. 1.4 - Prob. 25E Ch. 1.4 - Prob. 26E Ch. 1.4 - Prob. 27E Ch. 1.4 - Prob. 28E Ch. 1.4 - Prob. 29E Ch. 1.4 - Prob. 30E Ch. 1.4 - Prob. 31E Ch. 1.4 - Prob. 32E Ch. 1.4 - Prob. 33E Ch. 1.4 - Prob. 34E Ch. 1.4 - Prob. 35E Ch. 1.4 - Prob. 36E Ch. 1.4 - Prob. 37E Ch. 1.4 - Prob. 38E Ch. 1.4 - Prob. 39E Ch. 1.4 - Prob. 40E Ch. 1.4 - Prob. 41E Ch. 1.4 - Prob. 42E Ch. 1.4 - 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Knowledge Booster

A domain on which f is one-to-one and a formula for the inverse of f restricted to this domain. Sketch the graphs of f and f − 1 for the given exercise f ( z ) = z 3

A domain on which f is one-to-one and a formula for the inverse of f restricted to this domain. Sketch the graphs of f and f−1 for the given exercise f(z)=z3

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Chapter 1 Solutions

A domain on which $f$ is one-to-one and a formula for the inverse of $f$ restricted to this domain. Sketch the graphs of $f$ and $f^{- 1}$ for the given exercise $f (z) = z^{3}$