Question

if $f(x)=x^{2}+11$, then what is $(fcirc f)(x)$? choose the correct answer below. a. $x^{4}+22x + 121$ b. $x^{4}+22x^{2}+132$ c. $x^{4}+121$ d. $2x^{2}+11$ e. $2x^{2}+22$

Explanation:

Step1: Define composite function

$(f \circ f)(x) = f(f(x))$

Step2: Substitute $f(x)$ into itself

$f(f(x)) = f(x^2 + 11)$

Step3: Replace $x$ with $x^2+11$ in $f(x)$

$f(x^2 + 11) = (x^2 + 11)^2 + 11$

Step4: Expand the squared term

$(x^2 + 11)^2 = x^4 + 22x^2 + 121$

Step5: Add the constant term

$x^4 + 22x^2 + 121 + 11 = x^4 + 22x^2 + 132$

Answer:

B. $x^4 + 22x^2 + 132$