Inverse Functions

Front

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

Back

The x's and y's are switched.

Front

If the equation of f(x) goes through (1, 4) and (4, 6), what points does f⁻¹(x) go through?

Back

(4, 1) and (6, 4)

Front

Is the inverse function found correctly?

Back

Yes.

Front

Determine f⁻¹(2) given the following information about an invertible function, f(x): f(1) = -3, f(2) = -2, f(-1) = 2, f(3) = -1.

Back

-1

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

An inverse function reverses the operation of the original function.

Front

How do you find the inverse of a function algebraically?

Back

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

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 relationship between a function and its inverse?

Back

If f(a) = b, then f⁻¹(b) = a.

Front

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

Back

The function must be one-to-one (bijective).