Question

Let $f\left(x\right)=x^2-3x+4$, then the value of $x$ which satisfies $f\left(1\right)+f\left(x\right)=f\left(1\right)f\left(x\right)$ is

• A. $1$
• B. $2$
• C. $1or2$
• D. $1and0$

Answer 1

The correct option is C $1or2$

$f\left(x\right)=x^2-3x+4=0$

$\therefore f\left(1\right)=2$ and $x$ satisfies the condition $f\left(1\right)+f\left(x\right)=f\left(1\right)f\left(x\right)$
$\therefore 2+x^2-3x+4=2(x^2-3x+4)$ $\Rightarrow x^2-3x+2=0\Rightarrow x=1,x=2$