If \(f:R\to R\) is defined by \(f(x)=x^2-3x+2,find \,f(f(x)).\)
If \(f:R\to R\) is defined by \(f(x)=x^2-3x+2,find \,f(f(x)).\)
Solution and Explanation
It is given that \(f:R\to R \,is\,defined \,as f(x)=x^2-3x+2\).
\(f(f(x))=f(x^2-3x+2)\)
= \((x^2-3x+2)^2-3(x^2-3x+2)+2\)
= \(x^4+9x^2+4-6x^3-12x+4x^2-3x^2+9x-6+2\)
= \(x^4-6x^3+10x^2-3x\).
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