SOLUTION: Find f[f(-3)] when f(x) = x^2 + 1. Is this the same as f(f(x))?

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Question 1192968: Find f[f(-3)] when f(x) = x^2 + 1. Is this the same as f(f(x))?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39618) About Me  (Show Source):
Answer by ikleyn(52792) About Me  (Show Source):
You can put this solution on YOUR website!
.


            There are two questions in your post,  therefore,
            I give you two answers  (one answer for each question). 


(a)  To find f(f(-3)), first find f(-3) = (-3)^2 + 1 = 9 + 1 = 10.


     Then find f(f(-3)) by substituting the value of 10 instead of the interior "f(-3)" into the formula for f(x)

          f(f(-3))) = f(10) = 10^2 + 1 = 101.      


      It is the answer to your first question.



(b)  Next your question is whether f(f(-3)) is the same as f(f(x)).


     The answer is "NO", because f(f(-3)) is a number,

     while f(f(x)) is a polynomial function.

Solved, answered and thoroughly explained.


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Comment from student : Oh I was asking about the f[f(x)] If it was the same as f(f(x)) but thank you!



My response : No,  your second question was different.

                      Also,  I do not like when the  "THANKS"  comes in such curved form . . .