# Thread: What's the difference betwen inverse and reciprocal?

1. ## What's the difference betwen inverse and reciprocal?

Whats the difference or distinction?

2. 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

$
\frac{1}{2x+1}
$

3. Originally Posted by c_323_h
Whats the difference or distinction?
Given a function $f(x)$,

A function $g(x)$ such as $f(x)g(x)=1$ for all $f\not = 0$ is called the reciprocal function.

A function $g(x)$ such as $g(f(x))=f(g(x))=x$ for all $x$ is called the inverse function.