Question

given the function f(x) = x + 12. find (f ∘ f)(x).

○ x + 12

○ x + 24

○ x + 2

○ x + 6

Explanation:

Step1: Recall function composition

The composition \((f \circ f)(x)\) means \(f(f(x))\). So we first find \(f(x)\) and then substitute it into \(f\) again.
Given \(f(x)=x + 12\), to find \(f(f(x))\), we replace \(x\) in \(f(x)\) with \(f(x)\) itself.

Step2: Substitute \(f(x)\) into \(f\)

Substitute \(f(x)=x + 12\) into \(f\), so \(f(f(x))=f(x + 12)\).
Now, apply the function \(f\) to \(x + 12\): \(f(x + 12)=(x + 12)+12\).

Step3: Simplify the expression

Simplify \((x + 12)+12\) by combining like terms: \(x+12 + 12=x + 24\).

Answer:

\(x + 24\) (corresponding to the option "x + 24")