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

Suppose that $x^*$ means $5x^2 - x$. Then what does $(y+3)^*$ mean?

share|cite|improve this question
Are there parenthesis missing? Is that really $5\times 2$? If so, why not write $10$ instead? – Matt Sep 5 '12 at 13:35
@hardmath: Avoid editing the question until the OP has clarified the intended meaning. – Brandon Carter Sep 5 '12 at 13:38
5x^2 is correct. – Ctrl Sep 5 '12 at 13:39
up vote 2 down vote accepted

If $x^* = 5 x^2 - x$ then

$$(y+3)^* = 5(y+3)^2 - (y+3 )= 5(y^2 + 6 y + 9) - y - 3 = 5 y^2 + 29 y + 42 $$

share|cite|improve this answer
There's a sign error in the last expression (the x coefficient is net positive), but one character edits are not allowed! I leave it to your discretion. – hardmath Sep 5 '12 at 16:00
Thanks. Edited. – vanna Sep 5 '12 at 16:01
So, +42 is correct? – Ctrl Sep 5 '12 at 19:03
Yes. You can quickly check if this is correct by substituting $y$ to a particular value and look at what you get on the left-hand side and on the right-hand side. Try $y=-3$ you get $0$ on left and $5\times 9-29\times 3+42 = 0$ on right ;) – vanna Sep 6 '12 at 8:35

By 5x2 do you mean $5x^2$? In such a case, simply replace every instance of $x$ with $(y+3)$, and then expand.

For example, $f(x) = 2x+2 \Longrightarrow f(y+3) = 2(y+3)+2 = 2y+6+2 = 2y+8$.

share|cite|improve this answer

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.