Here is the function f(x) = 1/x, but I would like a different looking formula fo
ID: 3112435 • Letter: H
Question
Here is the function f(x) = 1/x, but I would like a different looking formula for it. I would like a formula that looks like f(x) = 1/1 - something. So, I could write it as f(x) = 1/1 - (1 - x). This equals but it just has a different form. Or, I might want it to look like f(x) = 1/1 - something with the addition that the something have a factor of "x-2". f(x) = 1/2 - (2 - x) But, it needs "1-", so factor out the 2 f(x) = 1/2(1 - (2 - x)/2) Whoops I have "2 - x". f(x) = 1/2(1 + (x - 2)/2) But, I want "something" in there, so I'll need a minus. f(x) = 1/2(1 - (-(x - 2)/2)) Whew! ok. I've got it. It has the "1-something" in the denominator and also the something has a factor of "x-2". It still equals 1/x, but I wanted it look a certain way. Do that again, but get the something to have a factor of "x + 3" in it.Explanation / Answer
f(x) = 1/x
f(x) = 1 / x+3 -3
factoring out -3 at the bottom
f(x) = 1 / -3 (- ( x+3/3 ) +1 )
or
f(x) = 1/ -3 ( 1 - ( x+3) / 3 )
f(x) = -1/3 ( 1 - ( x+3) / 3 )
this will give 1/x