Answer :

To solve the problem of finding [tex]f(g(2))[/tex], we need to follow these steps:


  1. Identify the functions:


    • [tex]f(x) = x^2 + 1[/tex]

    • [tex]g(x) = 3x[/tex]



  2. Find [tex]g(2)[/tex]:


    • Substitute [tex]x = 2[/tex] into [tex]g(x)[/tex]:
      [tex]g(2) = 3 \times 2 = 6[/tex]



  3. Use the result from [tex]g(2)[/tex] in [tex]f(x)[/tex]:


    • Since [tex]g(2) = 6[/tex], substitute [tex]x = 6[/tex] into [tex]f(x)[/tex]:
      [tex]f(6) = 6^2 + 1 = 36 + 1 = 37[/tex]



  4. Conclusion:


    • Therefore, [tex]f(g(2)) = 37[/tex].




The correct answer is [tex]\boxed{37}[/tex].

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