T Misconceptions Inverse of Functions

The video addresses common misconceptions about function inverses, including the belief that all functions have inverses, domain restrictions only apply to quadratics, and the composition of a function and its inverse always results in one. It also clarifies that vertical shifts in functions do not simply reverse in their inverses. The instructor uses examples like quadratic and trigonometric functions to illustrate these points.

Why does a quadratic function not have an inverse?

• It is not one-to-one.

• It is not a function.

• It does not pass the vertical line test.

• It is not continuous.

Which of the following functions also require domain restrictions to find their inverses?

• Absolute value functions

• Exponential functions

• Logarithmic functions

• Linear functions

What is the result of composing a function with its inverse?

• The original function

• One

• The identity element

• Zero

What is the identity element in the context of function inverses?

• Y

• X

• One

• Zero

How does a vertical shift in a function affect its inverse?

• It results in a reflection over the x-axis.

• It results in a horizontal shift.

• It results in a vertical shift in the opposite direction.

• It does not affect the inverse.

What is the correct reflection line for finding the inverse of a function?

• y = 0

• x = 0

• y = x

• x = y

Which of the following is a misconception about function inverses?

• Inverses are reflections over y = x.

• Every function has an inverse.

• Domain restrictions are necessary for some functions.

• The composition of a function and its inverse results in the identity element.