Inverse Functions

Front

What is an inverse function?

Back

An inverse function is a function that 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^-1(-25) = 7, what is f(7)?

Back

f(7) = -25.

Front

What does it mean to find the inverse of a function?

Back

Finding the inverse of a function means switching the x's and y's in the function's equation.

Front

How do you find the inverse of f(x) = 1/4x - 7?

Back

To find the inverse, switch x and y, then solve for y: y = 1/4x - 7 becomes x = 1/4y - 7, leading to f^-1(x) = 4x + 28.

Front

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

Back

The inverse is f^-1(x) = -1/4x - 3.

Front

What is the notation for an inverse function?

Back

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

Front

If f(a) = b, what is f^-1(b)?

Back

f^-1(b) = a.

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 across the line y = x.

Front

How can you verify if two functions are inverses?

Back

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

Front

What is the domain of an inverse function?

Back

The domain of the inverse function is the range of the original function.