5 Questions
If f(x) = 2x^2 + 3x - 1, what is the equation of the inverse function f^-1(x)?
x = ±√((y+1)/2 - 3/4)
What is the value of sin(2arcsin(1/2))?
√3/2
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
If f(x) = 2sin(x) and g(x) = 3cos(x), what is the value of f(g(arcsin(1/2)))?
3/2
What is the value of the expression cos(2arccos(1/3))?
-5/9
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
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.
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