Chapter 1 Section 5

Notes

Linguistic Mapping Exercises

Knowledge Checks

  1. Take \(f(x)=x^3.\) Draw the function on the restriction \((-3,-1]\cup[1,\infty)\).
  2. Take \(f\) and \(g\) to be functions with \(\mathcal{D}(f)=(-\infty,10]\), \(\mathcal{D}(g)=(-5,3]\cup (9,\infty)\), and the zero set of \(g\) is \(\{3,11\}\). Determine the domain of \(f+g\), \(fg\), and \(\frac{f}{g}\).
  3. Determine how \(f-g\) is defined and the domain of \(f-g.\)
  4. Take \(f\) and \(g\) to be given by \[f(x)=2x\quad\text{and}\quad g(x)=\sqrt{x-4}.\] Determine a formula for \(f\circ g\) and \(g\circ f\). Also determine the domain of both functions.
  5. Take \[a(x)=x,\quad b(x)=x^2,\quad c(x)=x+3,\quad d(x)=5x,\quad\text{and}\quad e(x)=\sqrt{x}.\] Decompose \(f\) into sums, products, quotients and or composites of more elementary functions, where \[f(x)=x^2\sqrt{x+5x^2}+\frac{x+3}{x}.\]
  6. Take \(f(x)=\frac{4x+1}{x-3}.\) Determine the domain and range of \(f\).

Remember, do the knowledge checks before checking the solutions.

Practice Problems

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