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

How do you find the inverse of a function algebraically?

Back

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

Front

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

Back

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

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.

Front

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

Back

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

Front

What is the graphical representation of an inverse function?

Back

The graph of an inverse function is a reflection of the original function across the line y = x.

Front

What is the relationship between a function and its inverse?

Back

If f is a function and f^-1 is its inverse, then f(f^-1(x)) = x and f^-1(f(x)) = x.

Front

What is the inverse of f(x) = x + 5?

Back

f^-1(x) = x - 5.

Front

What is the inverse of f(x) = 2x - 1?

Back

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

Front

What does the term 'one-to-one function' mean?

Back

A one-to-one function is a function where each output is produced by exactly one input, ensuring that the inverse is also a function.