Inverse Functions and Their Properties

The video tutorial by Anil Kumar covers inverse functions, including linear, quadratic, and rational functions. It explains when inverses exist, how to find them, and the importance of domain restrictions. The tutorial also includes practice questions on trigonometric inverses, emphasizing the conditions under which a function and its inverse are equal.

What is the main task introduced in the video regarding inverse functions?

• To memorize inverse function formulas

• To graph inverse functions

• To determine the truthfulness of statements about inverse functions

• To solve inverse function equations

What is the inverse of the function f(x) = 2x - 3?

• y = (x - 3) / 2

• y = 2x - 3

• y = (x + 3) / 2

• y = 2x + 3

Why does the inverse of f(x) = 2x^2 not exist?

• It passes the vertical line test

• It is not a polynomial

• It is a linear function

• It fails the horizontal line test

What method is used to find the inverse of f(x) = 2x^2 + 2x - 1?

• Graphing

• Substitution

• Completing the square

• Factoring

Under what condition is f(f^(-1)(x)) = x true?

• When f(x) is a quadratic function

• When f(x) is a one-to-one function

• When f(x) is a trigonometric function

• When f(x) is a polynomial

In the IB student example, what is the first step to find the inverse of a rational function?

• Differentiate the function

• Integrate the function

• Graph the function

• Swap x and y

What is the domain for the sine inverse function?

• 0 to π

• 0 to 2π

• -π/2 to π/2

• -π to π

What is the result of sin^(-1)(sin(π/3))?

• 2π/3

• π/6

• π/3

• 5π/6

What is the result of sin^(-1)(sin(5π/6))?

• π/3

• 2π/3

• π/6

• 5π/6

What is the domain for the cosine inverse function?

• 0 to π

• 0 to 2π

• -π/2 to π/2

• -π to π