Inverse of Functions

Front

What is the inverse of the function f(x) = -4x - 12?

Back

The inverse is f^{-1}(x) = 4x - 3.

Front

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

Back

It means the x's and y's are switched.

Front

How is the inverse of a function denoted?

Back

The inverse of the function f(x) is written as f^{-1}(x).

Front

Which of the following sets of values represents a function? (9,5) (10,5) (9,-5) (10,-5), (3,4) (4,-3) (7,4) (3, 8), (6,-5) (7, -3) (8, -1) (9, 1), (2, -2) (5, 9) (5, -7) (1, 4)

Back

(6,-5) (7, -3) (8, -1) (9, 1) is a function.

Front

Are the functions f(x) = 2x + 3 and g(x) = (x - 3)/2 inverses of each other?

Back

False.

Front

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

Back

Replace f(x) with y.

Front

If f(x) = 3x + 5, what is f^{-1}(x)?

Back

f^{-1}(x) = \frac{x - 5}{3}.

Front

What is the graphical representation of a function and its inverse?

Back

The graph of a function and its inverse are symmetric with respect to the line y = x.

Front

What is the domain of the inverse function if the range of the original function is {y | y > 0}?

Back

The domain of the inverse function is {x | x > 0}.

Front

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

Back

f^{-1}(x) = \sqrt{x}, x \geq 0.