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

2 Answers
Oct 26, 2017

1/(2x) - 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 = 1/(2x)
2xy = 1

x = 1/(2y)
...which is your inverse function. It's traditional to swap the variables, so, our inverse function is
y = 1/(2x)

...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(g(x)) = 1/(2(1/(2x)))
= 1/(1/x)

= x
GOOD LUCK

Oct 26, 2017

f’x. = 1/(2x)

Explanation:

f(x) = 1/(2x)

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

x = 1/(2y) switching x & y

y = 1/(2x)

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