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 back to x.

Front

How do you find the inverse of a function algebraically?

Back

To find the inverse of a function, replace f(x) with y, swap x and y, and then solve 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) = 2x + 3?

Back

The inverse is f⁻¹(x) = (x - 3)/2.

Front

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

Back

The inverse is f⁻¹(x) = (x - 4)/4.

Front

How do you verify if two functions are inverses of each other?

Back

To verify, check if f(f⁻¹(x)) = x and f⁻¹(f(x)) = x for all x in the domain.

Front

What is the domain of the inverse function if the original function has a range of [0, ∞)?

Back

The domain of the inverse function will be [0, ∞) since the range of the original function becomes the domain of the inverse.

Front

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

Back

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

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.