Inverse Functions

Front

What does it mean to find the inverse of a function?

Back

The x's and y's are switched.

Front

What is the inverse of the points (1,3)(2,4)(6,2)?

Back

(2,6)(3,1)(4,2)

Front

The inverse has been reflected over which line?

Back

y = x

Front

Find the inverse of f(x) = 1/4x - 7.

Back

f⁻¹(x) = 4x + 28

Front

What is the definition of an inverse function?

Back

A function that reverses the effect of the original function.

Front

If f(x) = 2x + 3, what is f⁻¹(x)?

Back

f⁻¹(x) = (x - 3)/2

Front

How do you verify if two functions are inverses?

Back

If f(f⁻¹(x)) = x and f⁻¹(f(x)) = x for all x in the domain.

Front

What is the graphical representation of an inverse function?

Back

It is a reflection of the original function over the line y = x.

Front

What is the inverse of the function f(x) = x² (for x ≥ 0)?

Back

f⁻¹(x) = √x.

Front

What happens to the domain and range when finding an inverse?

Back

The domain of the original function becomes the range of the inverse and vice versa.