008A Sample Final A, Question 2

Question: Find f(5) for f(x) given in problem 1.

Note: The function f(x) from problem 1 is: $f(x)=\log _{3}(x+3)-1$

Foundations
How would you find f(5) if f(x) = 2x + 1 instead?
Answer: we replace every occurrence of x with a 5. So
${\begin{array}{rcl}f(5)&=&2(5)+1\\&=&11\end{array}}$

Solution:

Step 1:
Replace any occurrence of x by 5, so
${\begin{array}{rcl}f(5)&=&\log _{3}(5+3)-1\\&=&\log _{3}(8)-1\end{array}}$

Final Answer:
$\log _{3}(8)-1$

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