if f(x+3)=2x^2−3x−1 find f(x+1)

wasangagac4 2022-10-14 Answered
if f ( x + 3 ) = 2 x 2 3 x 1 find f ( x + 1 )
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Answers (2)

zupa1z
Answered 2022-10-15 Author has 20 answers
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
Did you like this example?
Subscribe for all access
Chaim Ferguson
Answered 2022-10-16 Author has 4 answers
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 + 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.
Did you like this example?
Subscribe for all access

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more