How do you find the inverse of #f(x) = 4/x#?

1 Answer
Shantelle
May 12, 2018

The inverse is #x = 4/(f(x))# or #f(x) = 4/x#
(same as original)

Explanation:

To find the inverse, we swap the x and y values.

The original equation is #f(x) = 4/x#, meaning that the inverse would be #x = 4/(f(x))#.

If you want it with #f(x)# by itself, first multiply #f(x)# on both sides of the equation:
#x quadcolor(blue)(*quadf(x)) = 4/f(x) quadcolor(blue)(*quad(f(x))#

#x(f(x)) = 4#

Divide both sides by #color(blue)x#:
#(x(f(x)))/color(blue)x = 4/color(blue)x#

Therefore,
#f(x) = 4/x#

As you can see, the inverse is the same as the original equation. This can be proved by graphing both equations:
Graphing original #f(x) = 4/x#:
enter image source here

Graphing inverse #x = 4/f(x)#:
enter image source here
(desmos.com)

As you can see, both graphs are the same.

Hope this helps!

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