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Algebra and Trigonometry Functions

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Questions and Answers

If f(x) = 2x^2 + 3x - 1, what is the equation of the inverse function f^-1(x)?

x = ±√((y+1)/2 + 3/4)

x = ±√((y+1)/2 - 3/4) (correct)

x = ±√((y-1)/2 - 3/4)

x = ±√((y-1)/2 + 3/4)

What is the value of sin(2arcsin(1/2))?

√3/2 (correct)

1/2

1/√2

A parametric curve is defined by the equations x = 2t + 1, y = t^2 - 3. What is the equation of the Cartesian curve?

y = (x+1)^2 + 3

y = (x+1)^2 - 3

y = (x-1)^2 + 3

y = (x-1)^2 - 3 (correct)

If f(x) = 2sin(x) and g(x) = 3cos(x), what is the value of f(g(arcsin(1/2)))?

<p>3/2</p> Signup and view all the answers

What is the value of the expression cos(2arccos(1/3))?

<p>-5/9</p> Signup and view all the answers

Study Notes

Algebraic and Graphical Concepts

Uses algebraic and graphical concepts to model and solve problems involving functions and their inverses
Applies concepts to manipulate algebraic expressions and graphical functions to solve problems

Trigonometric Functions

Applies concepts and techniques of inverse trigonometric functions to solve problems
Simplifies expressions involving compound angles to solve problems

Technology in Problem-Solving

Uses appropriate technology to investigate, organize, and interpret information to solve problems in a range of contexts

Communication in Mathematics

Communicates mathematical ideas making comprehensive use of mathematical language, notation, diagrams, and graphs

Chapters and Topics

Inverse and Parametric Functions: chapters 6 and 7, covering topics 6.07, 6.08, 6.09, and 7.10
Further Trigonometric Identities and Inverse Trigonometric Functions: chapter 11

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Description

Test your skills in algebraic and graphical concepts, including functions and their inverses, trigonometric functions, and problem-solving strategies. This quiz covers various techniques and technologies used to investigate and interpret information.