Inverse Function Formative

Front

What is an inverse function?

Back

An inverse function is a function that reverses the effect of the original function. If the function f takes an input x and produces an output y, then the inverse function f⁻¹ takes y as input and produces x as output.

Front

How do you find the inverse of a function?

Back

To find the inverse of a function, first replace f(x) with y, then switch x and y, and finally solve for y.

Front

What does it mean to switch x and y in a function?

Back

Switching x and y means that for every point (x, y) in the original function, the point (y, x) will be in the inverse function.

Front

What is the first step in finding the inverse of a relation?

Back

The first step is to replace f(x) with y.

Front

What do you do after switching x and y when finding an inverse?

Back

After switching x and y, you solve for y.

Front

If f(x) = 2x + 3, what is f⁻¹(x)?

Back

f⁻¹(x) = (x - 3)/2.

Front

What is the 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

Can a function have more than one inverse?

Back

No, a function can have only one inverse if it is a one-to-one function.

Front

What is a one-to-one function?

Back

A one-to-one function is a function where each output is produced by exactly one input, meaning no two different inputs produce the same output.

Front

What is the inverse of the function f(x) = x² for x ≥ 0?

Back

The inverse is f⁻¹(x) = √x.