Inverse Functions

Front

What is an inverse function?

Back

An inverse function reverses the operation 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 back to x.

Front

How do you find the inverse of a function algebraically?

Back

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

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 over the line y = x.

Front

If f(x) = 2x + 3, what is f^-1(x)?

Back

f^-1(x) = (x - 3)/2.

Front

What is the first step to find the inverse of f(x) = -4x - 12?

Back

Swap x and y to get x = -4y - 12, then solve for y.

Front

What does it mean if f^-1(a) = b?

Back

It means that f(b) = a; b is the input that produces the output a in the function f.

Front

What is the relationship between a function and its inverse?

Back

A function and its inverse 'undo' each other. Applying a function followed by its inverse returns the original input.

Front

If f(3) = 10, what is f^-1(10)?

Back

f^-1(10) = 3.

Front

What is the importance of the line y = x in inverse functions?

Back

The line y = x is the line of reflection for a function and its inverse.

Front

How do you verify if two functions are inverses of each other?

Back

To verify, check if f(f^-1(x)) = x and f^-1(f(x)) = x for all x in the domain.