\( \def\dfrac#1#2{\displaystyle\frac{#1}{#2}} \def\solve#1{\begin{array}{rcl}#1\end{array} } \)

Home / 01 Mathematical Functions / 26 Using Tables for Combining Functions

Use the tables to answer the following questions.

\(\begin{{array}}{|c|c|} \hline\\ x & f(x)\\ \hline -6 & 2 \\ \hline -3 & 4\\ \hline 0 & -3\\ \hline 3 & 4\\ \hline 6 & 2\\ \\ \hline \end{{array}}\)
\(\begin{{array}}{|c|c|} \hline\\ x & g(x)\\ \hline -4 & -12 \\ \hline -2 & -3\\ \hline 0 & 1\\ \hline 2 & 3\\ \hline 4 & 12\\ \\ \hline \end{{array}}\)
\(\begin{{array}}{|c|c|} \hline\\ x & h(x)\\ \hline -12 & -6 \\ \hline -3 & -1.5\\ \hline 0 & 0\\ \hline 3 & 1.5\\ \hline 12 & 6\\ \\ \hline \end{{array}}\)
  1. Which of the above functions could even?
  2. Which of the above functions could odd?
  3. What is \(f(g(-2))\)?
  4. What is \(h(f(0))\)?
  5. What is \(h(g(-2))\)?
  6. What is \(f(h(-3))\)?

Solution

  1. Which of the above functions could even: \(f(x)\)
  2. Which of the above functions could odd: \(h(x)\). Note that if an odd function has 0 in its domain, then the output must be 0. Put another way, if 0 is in the domain, then \((0,0)\) is on the graph of the function.
  3. \(f(g(-2))=4\)
  4. \(h(f(0))=-1.5\)
  5. \(h(g(-2))=-1.5\)
  6. \(f(h(-3))=\text{{undefined}}\)