Inverse Tables

Front

What is an inverse function?

Back

An inverse function reverses the operation of the original function. If f(x) = y, then the inverse function f⁻¹(y) = x.

Front

Are the functions f(x) = 2x and g(x) = x/2 inverses of each other?

Back

Yes, because f(g(x)) = 2(x/2) = x and g(f(x)) = (2x)/2 = x.

Front

What is the inverse of the point (a, b)?

Back

The inverse of the point (a, b) is (b, a).

Front

True or False? The inverse of (3, 5) is (5, 3).

Back

True.

Front

True or False? The inverse of (8, 4) is (-8, -4).

Back

False.

Front

True or False? The inverse of (-5, 6) is (6, -5).

Back

True.

Front

What is the relationship between a function and its inverse?

Back

A function and its inverse 'undo' each other. Applying a function and then its inverse returns the original value.

Front

If f(x) = x + 3, what is f⁻¹(x)?

Back

f⁻¹(x) = x - 3.

Front

How do you find the inverse of a function algebraically?

Back

To find the inverse, replace f(x) with y, swap x and y, and solve for y.

Front

What is the inverse of the function f(x) = 2x + 1?

Back

f⁻¹(x) = (x - 1)/2.