Unraveling an Inverse FunctionDate: 11/30/2001 at 00:58:00 From: Trevor Lyons Subject: Inverse functions I had this question on a test and got it wrong. f(x) = -5x-2 ---- -x+1 the answer is y = -x-2 ---- -x+5 restriction cannot equal 5. I have no clue how to work this out, and would really like to know how to do it. Thanks, Trevor Date: 11/30/2001 at 01:18:18 From: Doctor Schwa Subject: Re: Inverse functions In other words, y = (-5x - 2) / (-x + 1). Then the inverse function is what "undoes" that; in other words, the opposite, turning y into x instead of x into y. So, the common way to find it is to switch x and y with each other in order to start "unraveling" the function: x = (-5y - 2) / (-y + 1). Now to solve for y, multiply both sides by (-y + 1) to get x (-y + 1) = -5y - 2 Distribute, -xy + x = -5y - 2 Collect all the y's on one side, and the rest of the terms on the other: -xy + 5y = -x - 2 Factor out the y, (-x + 5)y = -x - 2 and finally divide, y = (-x - 2) / (-x + 5) so -1 -x - 2 f (x) = -------- -x + 5 The restriction on x is that the denominator -x + 5 cannot equal zero, so x cannot equal 5. In other words, the domain of the inverse is all real numbers except 5. I hope that helps clear things up. If not, feel free to write back. - Doctor Schwa, The Math Forum http://mathforum.org/dr.math/ |
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