Hi all, can someone please give description about the use of composite and inverse functions with examples...? any help will be appreciated
I like to think of composit functions as one function inside another.
Consider $\displaystyle f(x)= x^2$ and $\displaystyle g(x) = \cos x$ then $\displaystyle f(g(x)) = g(x)^2 = (\cos x)^2$ is a composite function
For an inverse function, think about what the inverse of an operation is. If I square something the inverse operation is a square root. Therefore when thinking about functions i.e. $\displaystyle f(x) =x^2$ then the inverse is $\displaystyle f^{-1}(x) = \sqrt{x}$
"Square" and "square root" are not good examples here. For example, if x= -2, then $\displaystyle x^2= 4$ and then $\displaystyle \sqrt{4}= 2$, not -2. That's because [itex]f(x)= x^2[/itex] is not "one-to-one"- both $\displaystyle 2^2$ and $\displaystyle (-2)^2$ give four- so it does not have a true "inverse". A better example would be "cube" and "cube root". For any real number x, $\displaystyle \sqrt[3]{x^3}= \left(\sqrt[3]{2}\right)^3$.