Understanding Inverse Functions (5.1.1)

Question 1

• An inverse function “undoes” another function.
If g(x) is the inverse function of f(x), then g(f(x)) = x and f(g(x)) = x.

Answer 1

• An inverse function “undoes” another function.
If g(x) is the inverse function of f(x), then g(f(x)) = x and f(g(x)) = x.

Question 2

• An inverse function reverses the original function’s input and output values. For example, if g(x) is the inverse function of f(x) and f(a) = b, then it must be true that g(b) = a. In other words, if f(x) contains the coordinate pair (a, b), then g(x) must contain the coordinate pair (b, a).

Answer 2

• An inverse function reverses the original function’s input and output values. For example, if g(x) is the inverse function of f(x) and f(a) = b, then it must be true that g(b) = a. In other words, if f(x) contains the coordinate pair (a, b), then g(x) must contain the coordinate pair (b, a).

Question 3

• Not all functions have inverse functions.

Answer 3

• Not all functions have inverse functions.

Question 4

• The inverse function of f(x) is commonly written as f

–1(x), where the superscript –1 is not an exponent.

Answer 4

• The inverse function of f(x) is commonly written as f

–1(x), where the superscript –1 is not an exponent.