Inverse Functions

Front

What does it mean to find the inverse of a function?

Back

The x's and y's are switched.

Front

Given that f(x) = 3x + 5 and g(x) = 1/3x + 5, find f(g(x)). Are the two functions inverses of each other?

Back

f(g(x)) = x + 20; No, they are not inverses.

Front

Find the inverse of f(x)=2x-2.

Back

f^-1(x)=1/2x+1.

Front

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

Back

Switch x and y.

Front

What is the notation for the inverse of a function f(x)?

Back

f^-1(x).

Front

If f(x) = x^2, what is the inverse function?

Back

f^-1(x) = √x (for x ≥ 0).

Front

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

Back

Check if f(g(x)) = x and g(f(x)) = x.

Front

What is the inverse of the function f(x) = 5x - 3?

Back

f^-1(x) = (x + 3)/5.

Front

What happens to the domain of a function when you find its inverse?

Back

The domain of the original function becomes the range of the inverse function.

Front

What is the graphical representation of inverse functions?

Back

They are reflections over the line y = x.