if f ( x + 3 ) = 2 x 2 − 3 x − 1 find f ( x + 1 )

Question

if   f  (  x  +  3  )  =  2      x    2    −  3  x  −  1 find   f  (  x  +  1  )

zupa1z · Accepted Answer

You should change 2x - 9 too. Therefore,

𝑓 (𝑥 + 3) = (𝑥 + 3) (2 𝑥 - 9) + 26

𝑓 (𝑥 + 3) = (x + 3) (2 (x + 3) - 15) + 26

𝑓 (𝑥 + 1) = (x + 1) (2 (x + 1) - 15) + 26 = (x + 1) (2 x - 13) + 26 = 2 x^{2} - 11 𝑥 + 13

Chaim Ferguson · Accepted Answer

You have that   f  (  x  +  3  )  =  2      x    2    −  3  x  −  1. Write   y  =  x  +  3, then   x  =  y  −  3 and thus  f  (  y  )  =  2  (  y  −  3      )    2    −  3  (  y  −  3  )  −  1  =  2      y    2    −  15  y  +  26.Hence   f  (  x  +  1  )  =  2  (  x  +  1      )    2    −  15  (  x  +  1  )  +  26  =  2      x    2    −  11  x  +  13The key step is to first write x+3 as y and change all of the x&#039;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.

if f(x+3)=2x^2−3x−1 find f(x+1)

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