Inverse Functions

Front

What are inverse functions?

Back

Inverse functions are functions that reverse the effect 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 function algebraically?

Back

To find the inverse of a function algebraically, follow these steps: 1. Replace f(x) with y. 2. Swap x and y. 3. Solve for y. 4. Replace y with f^-1(x).

Front

What is the inverse of the function f(x) = 3x - 5?

Back

The inverse of the function f(x) = 3x - 5 is f^-1(x) = (x + 5) / 3.

Front

What is the inverse of the function f(x) = x⁴ - 2?

Back

The inverse of the function f(x) = x⁴ - 2 is f^-1(x) = ∜(x + 2).

Front

What is the inverse of the function f(x) = 1/4x - 7?

Back

The inverse of the function f(x) = 1/4x - 7 is f^-1(x) = 4x + 28.

Front

What is the graphical representation of inverse functions?

Back

The graphical representation of inverse functions is that they are reflections of each other across the line y = x.

Front

What is the relationship between a function and its inverse?

Back

A function and its inverse undo each other. If f(f^-1(x)) = x and f^-1(f(x)) = x, then f and f^-1 are inverses.

Front

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

Back

The domain of a function is the range of its inverse, and the range of a function is the domain of its inverse.

Front

What conditions must a function meet to have an inverse?

Back

A function must be one-to-one (bijective) to have an inverse. This means it must pass the horizontal line test.

Front

What is the horizontal line test?

Back

The horizontal line test is a method to determine if a function is one-to-one. If any horizontal line intersects the graph of the function more than once, the function does not have an inverse.