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

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

Back

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

Front

What is the relationship between a function and its inverse?

Back

A function and its inverse reflect over the line y = x.

Front

How do you find the inverse of a function algebraically?

Back

To find the inverse, replace f(x) with y, swap x and y, and solve for y.

Front

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

Back

If f(g(x)) = x and g(f(x)) = x for all x in the domain, then f and g are inverses.

Front

What is the domain of an inverse function?

Back

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

Front

What is the range of an inverse function?

Back

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

Front

If f(1) = 5, what is f^-1(5)?

Back

f^-1(5) = 1.

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) = x², is f^-1(x) a function?

Back

No, because f(x) = x² is not one-to-one; it fails the horizontal line test.