4.7 Inverse Linear Functions

Front

What is an inverse function?

Back

An inverse function reverses the operation of the original function. If f(x) takes an input x and produces an output y, then the inverse function f⁻¹(y) takes y and produces the original input x.

Front

How do you find the inverse of a linear function?

Back

To find the inverse of a linear function, swap the x and y variables and solve for y. For example, for f(x) = mx + b, the inverse is found by solving x = my + b for y.

Front

What is the graphical relationship between a function and its inverse?

Back

The graph of a function and its inverse are reflections of each other across the line y = x.

Front

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

Back

The inverse is f⁻¹(x) = (x - 4)/4.

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

How can you verify if two functions are inverses?

Back

To verify if two functions are inverses, compose them: if f(g(x)) = x and g(f(x)) = x, then they are inverses.

Front

What is the inverse of the relation {(7.4, -3), (4, -1), (0.6, 1), (-2.8, 3), (-6.2, 5)}?

Back

The inverse is {( -3, 7.4), (-1, 4), (1, 0.6), (3, -2.8), (5, -6.2)}.

Front

What is the inverse of the relation {(-4, -49), (8, 35), (-1, -28), (4, 7)}?

Back

The inverse is {(-49, -4), (35, 8), (-28, -1), (7, 4)}.

Front

What is the significance of the line y = x in relation to inverse functions?

Back

The line y = x serves as the line of reflection for the graphs of a function and its inverse.

Front

What is the domain of an inverse function?

Back

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