Answer: f( f(x) ) = x^4 + 2x^2 + 2
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Work Shown:
f(x) = x^2 + 1
f(x) = ( x )^2 + 1
f( f(x) ) = ( f(x) )^2 + 1 .. replace every x with f(x)
f( f(x) ) = ( x^2+1 )^2 + 1 .. plug in f(x) = x^2+1
f( f(x) ) = ( x^2+1 )( x^2+1 )+1
f( f(x) ) = y( x^2+1 )+1 .... let y = f(x) = x^2+1
f( f(x) ) = y*x^2+y+1 ... distribute
f( f(x) ) = x^2*( y ) + ( y ) + 1
f( f(x) ) = x^2*( x^2+1 ) + (x^2+1) + 1 .... plug in y = x^2+1
f( f(x) ) = x^4 + x^2 + x^2 + 1 + 1
f( f(x) ) = x^4 + 2x^2 + 2
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Side note: [tex]f(f(x)) = (f \circ f)(x)[/tex], the small circle indicates function composition. It's similar to [tex]f(g(x)) = (f \circ g)(x)[/tex]
