3rd Period Inverse Functions

Front

What is the notation for the inverse of a function?

Back

f^-1(x)

Front

How do you find the inverse of a function algebraically?

Back

1. Replace f(x) with y. 2. Swap x and y. 3. Solve for y. 4. Replace y with f^-1(x).

Front

If f(x) = 2x + 3, what is f^-1(x)?

Back

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

Front

What is the graphical relationship between a function and its inverse?

Back

The graph of a function and its inverse are reflections over the line y = x.

Front

If f(2) = 5, what is f^-1(5)?

Back

f^-1(5) = 2

Front

What is the inverse of f(x) = 3x - 9?

Back

f^-1(x) = (x + 9)/3

Front

What does it mean for a function to be one-to-one?

Back

A function is one-to-one if it passes the horizontal line test, meaning each y-value corresponds to exactly one x-value.

Front

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

Back

If f(g(x)) = x and g(f(x)) = x, then f and g are inverses.

Front

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

Back

f^-1(x) = √x

Front

What is the domain of the inverse function if the range of the original function is [0, ∞)?

Back

The domain of the inverse function is [0, ∞).