Inverses and Composition of Functions

Front

What is the process to graph the inverse of a function?

Back

Switch the x and y coordinates and plot the new points.

Front

What is the composition of functions f(g(x))?

Back

It is the result of applying function g to x, and then applying function f to the result of g.

Front

How do you find the inverse of a function?

Back

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

Front

What does it mean for two functions to be inverses of each other?

Back

If f(g(x)) = x and g(f(x)) = x for all x in the domain, then f and g are inverses.

Front

What is the inverse of f(x) = x^3 - 1?

Back

f^(-1)(x) = ∛(x + 1).

Front

If f(x) = 5x and g(x) = 2x - 1, what is f(g(x))?

Back

f(g(x)) = 10x - 5.

Front

What is the value of f(g(-2)) if f(x) = 2x - 5 and g(x) = -4x - 2?

Back

f(g(-2)) = 7.

Front

What is the definition of function composition?

Back

Function composition is the application of one function to the results of another, denoted as (f ∘ g)(x) = f(g(x)).

Front

What is the significance of the identity function in relation to inverses?

Back

The identity function is the output when a function is composed with its inverse.

Front

How do you verify if two functions are inverses?

Back

Check if f(g(x)) = x and g(f(x)) = x for all x in the domain.