Inverses of Functions

Front

What is the first step in finding the equation of the inverse of a function?

Back

Switch x and y.

Front

When two functions are inverses of each other, their graphs are reflective over...

Back

y = x.

Front

Are the blue and red graphs inverse functions?

Back

Yes.

Front

Are these the graphs of two inverse functions?

Back

Yes.

Front

To graph the inverse of a function...

Back

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

Front

What is an inverse function?

Back

A function that reverses the effect of the original 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

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

Front

How do you verify if two functions are inverses?

Back

Compose the functions and check if the result is the identity function.

Front

What is the graphical representation of an inverse function?

Back

The graph of the inverse function is a reflection of the original function across the line y = x.