Question

If f(x+1)=x^2+1,then f(x)= .(answer with explanation)

Answer 1

Answer:

$f(x) = x^{2}-2x+2$

Step-by-step explanation:

Given, $f(x+1) = x^{2} +1$

Put $x = y-1$

⇒ $f(y-1+1) = (y-1)^{2}+1$

or $f(y) = (y^{2}-2y+1)+1$         {∵$(a-b)^{2} = a^{2}-2ab+b^{2}$}

or $f(y) = y^{2}-2y+2$

⇒ $f(x) = x^{2}-2x+2$