Question

If $\left(x\right)=x^2-2x+4$ then the set of values of $x$ satisfying $f(x-1)=f(x+1)$ is

• A. $\{-1\}$
• B. $\{-1,1\}$
• C. $\left\{1\right\}$
• D. $\{1,2\}$

Answer 1

Answer: (C)

$\left\{1\right\}$

$f(x-1)=f(x+1)$

$⟹(x-1{)}^2-2(x-1)+4=(x+1{)}^2-2(x+1)+4$

$⟹x^2-2x+1-2x+2+4=x^2+2x+1-2x-2+4$

$⟹4x=4$

$⟹x=1$

Therefore, the answer is option (c)