# How do you find the inverse of f(x)=1/(2x)?

Oct 26, 2017

$\frac{1}{2 x}$ - this function is an inverse of itself!

#### Explanation:

Our inverse will be a function y = g(x) such that f(g(x)) = x

If we can manipulate our initial function so that, instead of y = some function of x, we have x = some function of y, we'll have our inverse.

$y = \frac{1}{2 x}$
$2 x y = 1$

$x = \frac{1}{2 y}$
...which is your inverse function. It's traditional to swap the variables, so, our inverse function is
$y = \frac{1}{2 x}$

...so this function is its own inverse!

We'll check our work. Subtitute our inverse function definition into our original equation, and calculate f(g(x)). We should get back x.

$f \left(g \left(x\right)\right) = \frac{1}{2 \left(\frac{1}{2 x}\right)}$
$= \frac{1}{\frac{1}{x}}$

$= x$
GOOD LUCK

Oct 26, 2017

f’x. = 1/(2x)

#### Explanation:

$f \left(x\right) = \frac{1}{2 x}$

$y = \frac{1}{2} x$ change f(x) to y.

$x = \frac{1}{2 y}$ switching x & y

$y = \frac{1}{2 x}$

:.f’(x) = 1/(2x) change y back to f’(x)