Answer:
Answer
Find out f(f(x)) .
To prove
As given in the question
f(x) = x² + 1
Now
f(f(x)) = f (x² + 1)
Now find out the value of f (x² + 1).
f(f(x)) = f (x² + 1)
= (x² + 1)² + 1
Using formula
(a + b)² = a² + b² + 2ab
Apply in the above function
f(f(x)) = (x² + 1)² + 1
f(f(x)) = [tex]x^{4}[/tex] + 1 + [tex]2x^{2}[/tex] + 1
Simplify
f(f(x)) = [tex]x^{4}[/tex] + [tex]2x^{2}[/tex] + 2
Thus the value of f(f(x)) is: f(f(x)) = [tex]x^{4}[/tex] + [tex]2x^{2}[/tex] + 2
Step-by-step explanation:
