12 HL Composite Functions Homework

Let \(f(x)=x^2\) and \(g(x)=x-1\).

  1. Find the range of \(f\) and \(g\), assuming the domain for both is \(\mathbb{R}\).
  2. Find the range of \(f\) and \(g\), assuming the domain for both is \([-2,\infty[\).
  3. Find the value of each of the functions below when \(x=4\).
    a) \(f\circ g\)
    b) \(g\circ f\)
  4. Find the range of each of the functions in Question 3.

Finding Derivatives

Here are a few questions to look at that involve applications of the new techniques and results (the chain rule, the product rule, and derivatives of exponential functions) we’re recently covered.

Make sure to start these before our next lesson, and aim to have them completed by Monday.

Pages 715–716 questions 3, 7, 9, 11

Pages 728 questions 1 a b e h i, 4, 6, 9, 10