Inverse Functions

Front

What is an inverse function?

Back

An inverse function reverses the effect of the original function, meaning if f(x) gives a result y, then f^-1(y) will return x.

Front

How do you find the inverse of a function?

Back

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

Front

What is the inverse of the function f(x) = 2x + 3?

Back

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

Front

If the domain of f(x) is x ≥ 4, what is the range of f^-1(x)?

Back

y ≥ 4.

Front

What is the inverse of the points (1, 3), (2, 4), (6, 8)?

Back

(3, 1), (4, 2), (8, 6).

Front

What does it mean for two functions to be inverses of each other?

Back

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

Front

How can you verify if two functions are inverses?

Back

By checking if f(g(x)) = x and g(f(x)) = x for all x in the domain.

Front

What is the graphical representation of inverse functions?

Back

The graphs of inverse functions are reflections of each other across 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 function?

Back

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