Flashcard: Inverse Functions

Front

What is the inverse of a function g(x)?

Back

g^-1(x)

Front

If f(x) goes through (1, 4) and (4, 6), what points does f^-1(x) go through?

Back

(4, 1) and (6, 4)

Front

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

Back

Switch x and y

Front

Are the functions f(x) and g(x) inverses of each other if f(g(x)) = x?

Back

Yes

Front

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

Back

f^-1(x) = (x-4)/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

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

Front

What is the graphical representation of inverse functions?

Back

They are reflections over the line y = x.

Front

What is the domain of the inverse function f^-1(x) if the range of f(x) is [a, b]?

Back

The domain of f^-1(x) is [a, b].

Front

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

Back

f^-1(x) = √x (for x ≥ 0).