A function's function

Level pending

If $f(x)=(18x^3+12x^2-189)^2$ , what is the digit sum of the value of $f(f(2))$ .

1 solution

Antony Diaz
Apr 28, 2014

First, we calculate $f(2)={ (18\cdot { 2 }^{ 3 }+12\cdot { 2 }^{ 2 }-189) }^{ 2 }={ 3 }^{ 2 }$ .

Then, $f(f(2))=f(9)$ and $f(9)={ (18\cdot { 9 }^{ 3 }+12\cdot { 9 }^{ 2 }-189) }^{ 2 }={ (13122+972-189) }^{ 2 }={ (13905) }^{ 2 }=193349025\\$

So the digit sum of this value is 36.