Inverse Functions Day 1

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 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, swap the x and y in the equation and solve for y.

Front

What is the inverse of f(x) = x² - 5?

Back

f⁻¹(x) = √(x + 5) for x ≥ 0.

Front

What is the notation for an inverse function?

Back

The notation for an inverse function is f⁻¹(x).

Front

If f(2) = 5, what is g(5) if g is the inverse of f?

Back

g(5) = 2.

Front

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

Back

Two functions f and g are inverses if f(g(x)) = x and g(f(x)) = x for all x in the domain.

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.

Front

If f(x) = x + 3, what is f⁻¹(-2)?

Back

f⁻¹(-2) = -5.

Front

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

Back

The domain of the original function is the range of its inverse and vice versa.

Front

How can you verify if two functions are inverses?

Back

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