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  4. Let f (x) =x2-3x+4, the value of x, which satisfies f (1) +f (x) = f (1) f (x), is

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Q. Let $f (x) =x^{2}-3x+4$, the value of x, which satisfies $f (1) +f (x) = f (1) f (x)$, is

Complex Numbers and Quadratic Equations

Solution:

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