Inverse Relations and Functions

Front

What is the definition of an inverse function?

Back

An inverse function is a function that reverses the effect of the original function, meaning if the function f takes an input x to an output y, then its inverse f⁻¹ takes y back to x.

Front

How do you find the inverse of a function algebraically?

Back

To find the inverse of a function algebraically, swap the x and y in the equation and then solve for y.

Front

What is the relationship between the domain of a function and the range of its inverse?

Back

The domain of the original function is the range of its inverse, and vice versa.

Front

What is the graphical representation of an inverse function?

Back

The graph of an inverse function is a reflection of the original function's graph across the line y = x.

Front

What is the domain of the inverse function if the original function has a range of {-7, -2, -1, 1, 4}?

Back

The domain of the inverse function is {-7, -2, -1, 1, 4}.

Front

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

Back

Two relations are inverses of each other if the output of one relation is the input of the other and vice versa.

Front

How can you determine if two relations are inverses?

Back

To determine if two relations are inverses, check if each pair of coordinates (x, y) in one relation corresponds to a pair (y, x) in the other relation.

Front

What is the domain of a function represented graphically as -3 ≤ x ≤ 3?

Back

The domain of the function is the set of all x-values that the function can take, which in this case is all values from -3 to 3, inclusive.

Front

What is the inverse of the coordinates (1, 2), (3, 8), (-3, 6)?

Back

The inverse of the coordinates is (2, 1), (8, 3), (6, -3).

Front

What is the significance of switching x's and y's when finding an inverse?

Back

Switching x's and y's is essential because it reflects the relationship of inputs and outputs in the function.