Question

f(x)=x/2-x. Find f(1/x)

Answer 1

Just plug in "1/x" in everywhere "x" shows up:
\[f(x)=f(1/x)=(1/x)/[2-(1/x)]\]

Answer 2

cool

Answer 3

what else

Answer 4

That reduces down to \[1/x(2-1/x) = 1/(2x-1)\]

Answer 5

how?

Answer 6

multiple both sides by x?

Answer 7

Starting with the original \[(1/x)/[2-(1/x)]\] it's just elementary math: instead of diving by [2-(1/x)], multiply by its reciprocal 1/[2-(1/x)]. So it will look like this: \[(1/x)/[2-(1/x)] = (1/x) * 1/[2-(1/x)] = 1/[x(2-(1/x))] = 1/(2x-x/x) = 1/(2x-1)\]

Answer 8

Oops, did that get cut off on the right side? The end is supposed to be 1/(2x-x/x) = 1/(2x-1)

Answer 9

thank you.

Answer 10

You're welcome. I hope it made sense! When you have fractions in both a numerator and denominator, multiplying by the denominator's reciprocal instead of leaving it as a division is a good way to simplify things.

Answer 11

:)