Question

If f(x+2)=x^2+4, then f(x)=?​

Answer 1

Answer:

has been provided or mentioned that a function F(x+1)=x^2–3x+2.

Interestingly, if we substitute a value of x-1 in the place of x, we obtain,

F((x-1)+1)=F(x)

Therefore, F(x)=(x-1)^2–3(x-1)+2=x^2–2x+1–3x+3+2=x^2–5x+6.

Hence, the function F(x) can be defined as x^2–5x+6.

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Answer 2

solution

solutionLet x+1=i

solutionLet x+1=iImplies x=i-1

solutionLet x+1=iImplies x=i-1Replace in above we get

solutionLet x+1=iImplies x=i-1Replace in above we getF(i)=(i-1)^2–3(i-1)+2

solutionLet x+1=iImplies x=i-1Replace in above we getF(i)=(i-1)^2–3(i-1)+2=i^2–2i+1–3i+3+2

solutionLet x+1=iImplies x=i-1Replace in above we getF(i)=(i-1)^2–3(i-1)+2=i^2–2i+1–3i+3+2=i^2–5i+6

solutionLet x+1=iImplies x=i-1Replace in above we getF(i)=(i-1)^2–3(i-1)+2=i^2–2i+1–3i+3+2=i^2–5i+6Therefore F(i)=i^2–5i+6

solutionLet x+1=iImplies x=i-1Replace in above we getF(i)=(i-1)^2–3(i-1)+2=i^2–2i+1–3i+3+2=i^2–5i+6Therefore F(i)=i^2–5i+6So F(x)=x^2–5x+6

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