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PS: Before posting it, one tried to grasp this (although didn't understand mfl's answer completely either).

I was shown the way to solve it: if I set $$\frac{3x-2}{2}=0 \Rightarrow x=\frac{2}{3} \Rightarrow x^2-x-1=-\frac{11}{9}$$ that answer will also be the one of $f(0)$ (i.e. $f(0)=-11/9$), which is true, but I don't quite get it: how the answer of $f(\frac{3x-2}{2})$ (i.e. $-11/9$) is also the answer of $f(0)$? why the answer of the quad equ. is also the answer of $f(0)$ (that it is $f(0)=-11/9$)? I asked the person who solved it for me if there was a proof for this, but she couldn't bring it. So, I would be very happy and obliged if someone here would show the proof that it is $f(0)=-11/9$.

user36339
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  • For what it's worth, the question you linked to needs to be solved a bit differently than this one. – John Dec 08 '17 at 19:38

2 Answers2

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substituting $$t=\frac{3x-2}{3}$$ then we get $$x=\frac{2t+2}{3}$$ then we get $$f(t)=\left(\frac{2t+2}{3}\right)^2-\frac{2+2t}{3}-1$$ then we get ...?

Dr. Sonnhard Graubner
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Hint: To calculate $f(0)$ given an expression for $f((3x-2)/2)$, you could find the value of $x$ that makes the argument zero, and then use that value in the expression.

John
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  • yes, I knew that but I meant why the answer of the quad equ. is also the answer of $f(0)$? – user36339 Dec 08 '17 at 18:39
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    I don't think that's true. The right side is an expression for $f((3x-2)/2)$, not $f(x)$. – John Dec 08 '17 at 19:20
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    Put another way, $x=2/3$ gives you the solution for $f(0)$, because $(3x-2)/2 = 0$ when $x=2/3$. – John Dec 08 '17 at 19:30