Answer :

Sure! Let's solve the given problem step by step.

We are given the function [tex]\(f(x) = 2 + 6x\)[/tex] and need to find the value of [tex]\(f(f(-2))\)[/tex].

First, let's find [tex]\(f(-2)\)[/tex]:
1. Substitute [tex]\(-2\)[/tex] into the function [tex]\(f(x)\)[/tex]:
[tex]\[
f(-2) = 2 + 6(-2)
\][/tex]
2. Calculate the value inside the parenthesis:
[tex]\[
6 \times (-2) = -12
\][/tex]
3. Add 2 to -12:
[tex]\[
f(-2) = 2 + (-12) = 2 - 12 = -10
\][/tex]

So, [tex]\(f(-2) = -10\)[/tex].

Next, we need to find [tex]\(f(f(-2))\)[/tex], which means we need to find [tex]\(f(-10)\)[/tex]:
1. Substitute [tex]\(-10\)[/tex] into the function [tex]\(f(x)\)[/tex]:
[tex]\[
f(-10) = 2 + 6(-10)
\][/tex]
2. Calculate the value inside the parenthesis:
[tex]\[
6 \times (-10) = -60
\][/tex]
3. Add 2 to -60:
[tex]\[
f(-10) = 2 + (-60) = 2 - 60 = -58
\][/tex]

Therefore, [tex]\(f(f(-2)) = -58\)[/tex].

So, the correct answer is [tex]\(-58\)[/tex].

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Rewritten by : Barada