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

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    5x^2 is correct.2012-09-05

2 Answers 2

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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 $

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    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 ;)2012-09-06
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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, $f(x) = 2x+2 \Longrightarrow f(y+3) = 2(y+3)+2 = 2y+6+2 = 2y+8$.