Gr12 Mathematics: Ch 2.2 Inverse Functions

What is the primary condition for a function to have an inverse that is also a function?

The function must be continuous

The function must be one-to-one (correct)

The function must be non-linear

The function must be many-to-one

What is the graphical representation of a function and its inverse?

They are symmetrical about the line y = x (correct)

They are asymmetrical

They are symmetrical about the y-axis

They are symmetrical about the x-axis

What does the notation f^(-1)(x) indicate?

The reciprocal of f(x)

The inverse function (correct)

The square root of f(x)

The derivative of f(x)

How do you find the inverse function of a given function?

Interchange x and y, and then solve for y Signup and view all the answers

What is the purpose of the horizontal line test?

To determine if a function has an inverse that is also a function Signup and view all the answers

What is the relationship between a function and its inverse?

They undo each other's operations Signup and view all the answers

If a function is many-to-one, what can be said about its inverse?

It cannot be uniquely defined Signup and view all the answers

What is the result of applying a function and its inverse in succession?

The original input is recovered Signup and view all the answers

Why is the graphical symmetry of a function and its inverse important?

It helps in visualizing the relationship between the function and its inverse Signup and view all the answers

What is the significance of the horizontal line test?

It determines if a function is one-to-one Signup and view all the answers

What happens when you interchange x and y in the equation y = f(x)?

You get the equation of the inverse function Signup and view all the answers

What is the relationship between the graphs of a function and its inverse?

They are symmetrical about the line y = x Signup and view all the answers

Which of the following statements about inverse functions is false?

The notation f^(-1)(x) indicates the reciprocal of f(x). Signup and view all the answers

What is the consequence of a function failing the horizontal line test?

The function is many-to-one. Signup and view all the answers

Why is it important to check if a function is one-to-one before finding its inverse?

To ensure the inverse is also a function. Signup and view all the answers

What is the purpose of solving for y when finding the inverse of a function?

To express the inverse function in terms of y. Signup and view all the answers

What is the relationship between the graphs of a function and its inverse when reflected across the line y = x?

They are symmetrical. Signup and view all the answers

What is the result of applying a function and its inverse in succession, with the original input being x?

x Signup and view all the answers