Operations on functions

  1. \rhd  Adding functions (2:32)  For f(x)=9-x^2 and g(x) = 5x^2+2x+1, Sal finds (f+g)(x).
  2. \rhd  Subtracting functions (2:16)  For f(x)=2x\sqrt 5-4 and g(x) = x^2+2x\sqrt 5-1, Sal finds (f-g)(x).
  3. \rhd  Multiplying functions (2:59) For f(x)=7x-5 and g(x) = x^3+4x, Sal finds (fg)(x).
  4. \rhd  Dividing functions (6:17) For f(x)=2x^2+15x-8 and g(x) = x^2+10x+16, Sal finds \left(\dfrac{f}{g}\right)(x).
  5. \rhd  Intro to composing functions (6:14) Three functions are given: f(x)=x^2-1g(x) given by a table, and h(x) whose graph is provided. Sal finds f(g(2)), f(h(2)), and h(g(f(2))).
  6. *  Practice: Type of problem: For g(x) =\dfrac{3x-5}{x+1} and h(y) = \sqrt{1-3y}, evaluate h(g(0)).
  7. \rhd  Evaluating composite functions (4:09) For g(x)=x^2+5x-3 and g(y)= 3(y-1)^2-5, Sal finds (h\circ g)(-6).
  8. \rhd  Finding composite functions (2:56) For f(x) = \sqrt{x^2-1} and g(x) = \dfrac{x}{1+x}, Sal finds f(g(x)) and g(f(x)).
  9. *  Practice: Type of problem: For f(x) = x^3-6 and h(x) = \sqrt[3]{2x-15}, find a formula for f(h(x)).