Inverses of Linear Functions

Front

What is the definition of the inverse of a function?

Back

The inverse of a function is a function that reverses the effect of the original function. If the function is denoted as f(x), its inverse is denoted as f^{-1}(x), such that f(f^{-1}(x)) = 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 f^{-1}(x) = (x - b)/m.

Front

What is the inverse of the relation {(-2,0), (3,4), (5,7)}?

Back

The inverse of the relation is {(0,-2), (4,3), (7,5)}.

Front

What is the inverse of the function f(x) = 4x - 5?

Back

The inverse of the function is f^{-1}(x) = \frac{x + 5}{4}.

Front

What is the general form of a linear function?

Back

The general form of a linear function is f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

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

Back

Two functions are inverses of each other if applying one function to the result of the other function returns the original input.

Front

How can you verify that two functions are inverses?

Back

To verify that two functions f(x) and g(x) are inverses, check if f(g(x)) = x and g(f(x)) = x for all x in the domain.

Front

What is the inverse of the function f(x) = 5(x + 6)?

Back

The inverse of the function is f^{-1}(x) = \frac{x}{5} - 6.

Front

What is the slope of the line represented by the function f(x) = 3x + 2?

Back

The slope of the line is 3.

Front

What is the y-intercept of the function f(x) = -2x + 4?

Back

The y-intercept of the function is 4.