Verified 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
\(f(f(x)) = x^{4} +1 +2x^{2}+ 1\)
Simplify
\(f(f(x)) = x^{4} +2x^{2}+ 2\)
Thus the value of f(f(x)) is \(f(f(x)) = x^{4} +2x^{2}+ 2\) .
You can use the given function's definition and put that as input in the given function to evaluate function of function.
The expression for f(f(x)) is
\(f(f(x)) = x^4 + 2x^2 + 2\)
How to evaluate function of functions?
We pass the output of the first function as input to the second function.
Suppose the given functions are
\(f(x)\) and \(g(x)\)
Then the function of functions for "g" taking input as "f" is written as
\(g(f(x)) = g \circ f(x)\\f(g(x)) = f \circ g(x)\)
This above is the notation we use to write composite functions.
Thus, as the given function is
\(f(x) = x^2 + 1\)
So, the function of function would be:
\(f(f(x)) = (f(x))^2 + 1 = (x^2 + 1)^2 + 1 = x^4 + 2x^2 + 1 + 1 \\\\f(f(x)) = x^4 + 2x^2 + 2\)
The expression for f(f(x)) is
\(f(f(x)) = x^4 + 2x^2 + 2\)
Learn more about composite functions here:
https://brainly.com/question/24780056