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

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Answer 1 · 2017-10-26T01:58:33

#1/(2x)# - this function is an inverse of itself!

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

Answer 2 · 2017-10-26T02:00:08

#f’x. = 1/(2x)#

#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)