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What are inverse functions?

These inverse functions are also calledarccosxandarctanx,and you can ?nd out more about them in the unit on Trigonometric Functions. Some functions cannot have inverses, even if we restrict their domains. For example, a constantfunction cannot have an inverse.

How do you draw a graph of an inverse function?

sketch the graph of an inverse function using the graph of theoriginal function. Introduction f(x) =y. inverse function, which we call f?1, is another function that takesyback tox. So f?1(y) =x. For f?1 to be an inverse of f, this needs to work for everyxthatf acts upon. The inverse of the functionfis the function that sends eachf(x)back tox.

How do you reverse a function?

One way to work out an inverse function is to reverse the operations thatf carries out on anumber. Here is a simple example. We shall setf(x) = 4x, so thatf takes a number xandmultiplies it by 4:f(x) = 4x (multiply by 4). We want to de?ne a function that will take 4 timesx, and send it back tox. This is the sameas saying thatf?1(x)dividesxby 4. So