Inverse Functions Notes Review

Front

How can you find the inverse of a function algebraically?

Back

Replace f(x) with y, swap x and y, then solve for y.

Front

What happens when you reflect a point over the line y = x?

Back

The x-coordinate and y-coordinate swap places.

Front

Which of the following statements is true about the horizontal line test?

Back

It determines if a function is one-to-one.

Front

What is the inverse of the function f(x) = 3x + 6?

Back

f^(-1)(x) = (1/3)x - 2.

Front

What is the inverse of the function g(x) = (1/3)x - 2?

Back

g^(-1)(x) = 3x + 6.

Front

Define an inverse function.

Back

An inverse function reverses the operation of the original function.

Front

What is the graphical representation of an inverse function?

Back

The graph of an inverse function is a reflection of the original function across the line y = x.

Front

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

Back

A function must be one-to-one (bijective) to have an inverse.

Front

How do you verify if two functions are inverses of each other?

Back

If f(g(x)) = x and g(f(x)) = x for all x in the domain.

Front

What is the inverse of the function f(x) = x^2 (for x >= 0)?

Back

f^(-1)(x) = √x.