Inverses

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 to an output y, then the inverse function f⁻¹ takes y back to x.

Front

How do you find the inverse of a function?

Back

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

Front

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

Back

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

Front

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

Back

Two functions are inverses if applying one function followed by the other returns the original input.

Front

If f(x) = 2x + 3, what is f⁻¹(x)?

Back

f⁻¹(x) = (x - 3)/2.

Front

What is the graphical representation of inverse functions?

Back

Inverse functions are reflections of each other over the line y = x.

Front

What is the importance of restricting the domain of a function when finding its inverse?

Back

Restricting the domain ensures that the inverse function is also a function, meaning it passes the vertical line test.

Front

If f(x) = x², what is the inverse function?

Back

f⁻¹(x) = √x, but the domain must be restricted to x ≥ 0.

Front

What is the inverse operation of addition?

Back

Subtraction.

Front

What is the inverse operation of multiplication?

Back

Division.