Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I would like to get x from the following function when the y is known and which + means If $1$ is bigger than x its equal $ 1 - x$ and else it's equal zero. Also, + means If x is bigger than 5 its equal $x-5$ and else it's equal zero:

$$ 0.1 x + (\frac{1}{2} - \frac{(1-x)_{+}^2}{2}) + (\frac{(x-5)^{2}_{+}}{2}) = -\log(1-y)$$

share|cite|improve this question

Write the left side as $$f(x)=\begin {cases} \frac 12(\frac x5+2x-x^2)&x \lt 1\\ \frac x{10}+\frac 12&1 \le x \lt 5\\ \frac 12(x^2-9.8x+26)&x \ge 5 \end {cases}$$ Given the right side, you can solve each of these and see if $x$ is in the correct range.

share|cite|improve this answer
Can you check your answer. I think , the first equation is right, the second should be 0.1x+0.5 , and the third should be 0.5(x^2-1.8x+26). Am I right or wrong? – rose Jun 18 '14 at 0:20
@rose: you are correct on the second. For the third, the $\frac 12(x-5)^2$ contributes $-\frac {10}2x$ and the leading $0.1x$ contributes $\frac 12(0.2x)$ – Ross Millikan Jun 18 '14 at 2:08

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.