Inverse Functions

Front

What is an inverse function?

Back

An inverse function reverses the operation of the original function, such that if f(x) = y, then f^-1(y) = x.

Front

How do you find the inverse of a function algebraically?

Back

To find the inverse, swap the x and y in the equation and solve for y.

Front

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

Back

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

Front

What is the notation for an inverse function?

Back

The notation for an inverse function is f^-1(x).

Front

If f(x) = x - 4, what is f^-1(x)?

Back

f^-1(x) = x + 4.

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

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

Back

f^-1(x) = x/5.

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.

Front

If f(x) = x², is f^-1(x) defined for all x?

Back

No, f^-1(x) is not defined for all x because f(x) is not one-to-one.

Front

What is the inverse of a linear function?

Back

The inverse of a linear function is also a linear function, provided the original function is one-to-one.