Hello,
![-20 \leq 3x+1 \leq 10\\ \Rightarrow\ -21 \leq 3x \leq 9\\ \Rightarrow\ -7 \leq x \leq 3\\ Sol=[-7\ 3]\ if\ x\ is\ a\ real. ](https://tex.z-dn.net/?f=-20%20%5Cleq%203x%2B1%20%5Cleq%2010%5C%5C%0A%5CRightarrow%5C%20-21%20%5Cleq%203x%20%5Cleq%209%5C%5C%0A%5CRightarrow%5C%20-7%20%5Cleq%20x%20%5Cleq%203%5C%5C%0A%0ASol%3D%5B-7%5C%203%5D%5C%20if%5C%20x%5C%20is%5C%20a%5C%20real.%0A)
F(x) = x2 + 1 f(f(x))
2 answers:
<h3>Answer: f( f(x) ) = x^4 + 2x^2 + 2</h3>
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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: , the small circle indicates function composition. It's similar to
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