Lesson 3.6 - Inverse Functions

Front

What is an inverse function?

Back

An inverse function reverses the operation of the original function. If f(x) takes an input x and produces an output y, then the inverse function f⁻¹(y) takes y and produces the original input x.

Front

How do you determine if two functions are inverses of each other?

Back

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

Front

What is the notation for an inverse function?

Back

The notation for an inverse function is f⁻¹(x), which is read as 'f inverse of x'.

Front

If f(x) = 3x - 5, what is f⁻¹(x)?

Back

f⁻¹(x) = (x + 5)/3.

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 composition of functions?

Back

The composition of functions f and g, denoted as f(g(x)), is the application of g first, followed by f.

Front

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

Back

No, f(x) = x² is not one-to-one, so it does not have an inverse unless restricted to x ≥ 0.

Front

What is the inverse of the function f(x) = 2x + 4?

Back

f⁻¹(x) = (x - 4)/2.

Front

If f(1) = 3, what is f⁻¹(3)?

Back

f⁻¹(3) = 1.

Front

What points does f⁻¹(x) go through if f(x) goes through (2, 5)?

Back

f⁻¹(x) goes through (5, 2).