# if f(x+3)=2x^2−3x−1 find f(x+1)

wasangagac4 2022-10-14 Answered
if $f\left(x+3\right)=2{x}^{2}-3x-1$ find $f\left(x+1\right)$
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## Answers (2)

zupa1z
Answered 2022-10-15 Author has 20 answers
You should change 2x - 9 too. Therefore,
$𝑓\left(𝑥+3\right)=\left(𝑥+3\right)\left(2𝑥-9\right)+26$
$𝑓\left(𝑥+3\right)=\left(x+3\right)\left(2\left(x+3\right)-15\right)+26$
$𝑓\left(𝑥+1\right)=\left(x+1\right)\left(2\left(x+1\right)-15\right)+26=\left(x+1\right)\left(2x-13\right)+26=2{x}^{2}-11𝑥+13$
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Chaim Ferguson
Answered 2022-10-16 Author has 4 answers
You have that $f\left(x+3\right)=2{x}^{2}-3x-1$. Write $y=x+3$, then $x=y-3$ and thus
$f\left(y\right)=2\left(y-3{\right)}^{2}-3\left(y-3\right)-1=2{y}^{2}-15y+26.$
Hence $f\left(x+1\right)=2\left(x+1{\right)}^{2}-15\left(x+1\right)+26=2{x}^{2}-11x+13$
The key step is to first write x+3 as y and change all of the x's to y−3. In this way you rewrite the equation so that you get f(y) in terms of y. Then you can replace y by whatever you like.
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