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Mark (√) against the correct answer in the following:

Question:

Mark (√) against the correct answer in the following:

If $f(x)=x^{2}-3 x+2$ then (f of) $(x)=?$

A. $x^{4}$

B. $x^{4}-6 x^{3}$

C. $x^{4}-6 x^{3}+10 x^{2}$

D. None of these

Solution:

$f(x)=x^{2}-3 x+2$

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

$\Rightarrow f(x)=(x-2)(x-1)$

$\Rightarrow f(x)=(x-2)(x-1)$

$\Rightarrow f(f(x))=(f(x)-2)(f(x)-1)$

$\Rightarrow f(f(x))=((x-2)(x-1)-2)((x-2)(x-1)-1)$

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

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

$\Rightarrow f(f(x))=x^{4}-3 x^{3}+x^{2}-3 x^{3}+9 x^{2}-3 x$

$\Rightarrow f(f(x))=x^{4}-6 x^{3}+10 x^{2}-3 x$

 

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