Question

If $f\left(x\right)=x^2-2x+4$ 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

The correct option is C $\left\{1\right\}$

Given $f\left(x\right)=x^2-2x+4=(x-1{)}^2+3$

It is also given that, $f(x-1)=f(x+1)$

$\Rightarrow (x-1-1{)}^2+3=(x+1-1{)}^2+3$

$\Rightarrow (x-2{)}^2=x^2$

$\Rightarrow x-2=\pm x$

$\Rightarrow x-2=x$ or $x-2=-x$

$\Rightarrow -2=0$ or $x+x=2\Rightarrow x=1$

So the only solution is $\left\{1\right\}$