008A Sample Final A, Question 2

Question: Find f(5) for Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f(x) = \log_3(x) - 1} , which is the function from problem 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
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \begin{array}{rcl} f(5) &= &2(5) + 1\\ & =& 11 \end{array}}

Solution:

Step 1:
Replace any occurrence of x by 5, so
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \begin{array}{rcl} f(5) &=& \log_3(5 + 3) - 1 \\ &=& \log_3(8) - 1 \end{array}}

Final Answer:
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \log_3(8) - 1}

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