Inverse Functions

Front

What is an inverse function?

Back

An inverse function reverses 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 back to x.

Front

If f(2) = -1, what is g(-1)?

Back

g(-1) = 2, because f and g are inverse functions.

Front

What is the relationship between a function and its inverse?

Back

For a function f and its inverse f⁻¹, the following holds: f(f⁻¹(x)) = x and f⁻¹(f(x)) = x for all x in the domain.

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 inverse of f(x) = 3x + 5?

Back

f⁻¹(x) = (x - 5)/3.

Front

If f⁻¹(-25) = 7, what is f(7)?

Back

f(7) = -25, because f and f⁻¹ are inverse functions.

Front

What does it mean if two functions are inverses of each other?

Back

It means that applying one function followed by the other returns the original input.

Front

What is the inverse of f(x) = -4x - 12?

Back

f⁻¹(x) = -1/4x - 3.

Front

If g(1) = -2, what is f(-2)?

Back

f(-2) = 1, because f and g are inverse functions.

Front

What is the graphical representation of inverse functions?

Back

The graphs of inverse functions are reflections of each other across the line y = x.