Inverse Functions

Front

What is an inverse function?

Back

An inverse function reverses the operation of the original function. 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

What is the relationship between the graphs of a function and its inverse?

Back

The graphs of a function and its inverse are reflections of each other across the line y = x.

Front

What is the domain of a function?

Back

The domain is the set of all possible input values (x-values) for the function.

Front

What is the range of a function?

Back

The range is the set of all possible output values (y-values) for the function.

Front

If f(x) = 2x + 3, what is f⁻¹(x)?

Back

f⁻¹(x) = (x - 3)/2.

Front

What does it mean for two functions to be inverses?

Back

Two functions f and g are inverses if f(g(x)) = x and g(f(x)) = x for all x in their domains.

Front

How do you verify if two functions are inverses?

Back

To verify, check if f(g(x)) = x and g(f(x)) = x.

Front

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

Back

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

Front

What is the significance of the point (x, y) in relation to inverse functions?

Back

If (x, y) is on the graph of f, then (y, x) is on the graph of f⁻¹.