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  4. If f(x+(1/x))=x3+(1/x3)-7(x+(1/x)), then the value of (fof) (3) equals

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Q. If $f\left(x+\frac{1}{x}\right)=x^3+\frac{1}{x^3}-7\left(x+\frac{1}{x}\right)$, then the value of (fof) (3) equals

Relations and Functions - Part 2

Solution:

Let $x +\frac{1}{ x }= t$
$f(t)=t^3-10 t $
$f(3)=27-30=-3 $
$(f \circ f)(3)=f(f(3))=f(-3)=-27+30=3$