Whats the difference or distinction?
reciprocal simply means 1 over
the reciprocal of x is 1/x
the reciprocal of something like √x is 1/√x
inverse is the "opposite" of the function
the inverse of √x is x² since the square and the root effectively 'undo' each other
2x + 1 woudl have and inverse of ½(x - 1)
the reciprocal woudl be
$\displaystyle
\frac{1}{2x+1}
$
Given a function $\displaystyle f(x)$,Originally Posted by c_323_h
A function $\displaystyle g(x)$ such as $\displaystyle f(x)g(x)=1$ for all $\displaystyle f\not = 0$ is called the reciprocal function.
A function $\displaystyle g(x)$ such as $\displaystyle g(f(x))=f(g(x))=x$ for all $\displaystyle x$ is called the inverse function.