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  4. Let f(x)=x2-6 x+8, then number of real roots of the equation f(f(x))=0 is

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Q. Let $f(x)=x^2-6 x+8$, then number of real roots of the equation $f(f(x))=0$ is

Relations and Functions - Part 2

Solution:

$f(x)=x^2-6 x+8$
$f ( f ( x ))=0 \Rightarrow f ( x )=2$ or $f ( x )=4$
$\Rightarrow f ( f ( x ))=0$ has four distinct real roots.