Let f (x) = x^2 + 5. Find formulas for f (f (x)) and f (f (f (x)))

F (f (x)) means subsitute f (x) or x^2+5 for x in the other one

f (f (x)) = (f (x)) ^2+5

f (x^2+5) = (x^2+5) ^2+5

f (f (x)) = x^4+10x^2+25+5

f (f (x)) = x^4+10x^2+30

f (f (f (x)))

just subsitutte f (f (x)) for x in f (x)

f (f (f (x))) = (x^4+10x^2+30) ^2+5

f (f (f (x))) = (x^4+10x^2+30) ^2+5

f (f (f (x))) = x^8+20x^6+150x^4+500x^2+625+5

f (f (f (x))) = x^8+20x^6+150x^4+500x^2+630

so

f (f (x)) = x^4+10x^2+30

f (f (f (x))) = x^8+20x^6+150x^4+500x^2+630