Inverses

Front

What is the inverse of a function?

Back

The inverse of a function f(x) is a function that reverses the effect of f. If f(x) = y, then f^-1(y) = x.

Front

How do you denote the inverse of a function g(x)?

Back

The inverse of g(x) is denoted as g^-1(x).

Front

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

Back

Switch x and y in the equation.

Front

What does it mean for two functions to be inverses of each other?

Back

Two functions f and g are inverses if f(g(x)) = x and g(f(x)) = x for all x in the domain.

Front

Can a function have more than one inverse?

Back

No, a function can have at most one inverse if it is a one-to-one function.

Front

What is a one-to-one function?

Back

A one-to-one function is a function where each output is produced by exactly one input.

Front

Given f(x) = 2x + 3, find f^-1(x).

Back

f^-1(x) = (x - 3)/2.

Front

What is the inverse of the points (1,3), (2,4), (6,8)?

Back

The inverse is (3,1), (4,2), (8,6).

Front

Is f^-1(x) a function if f(x) = {(3, 7), (4, -2), (5, -1), (8, 7)}?

Back

No, f^-1(x) is not a function because the output 7 corresponds to two different inputs (3 and 8).

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.