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: $f(x)=x^2-1$, $g(x)$ 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 $f(h(x))$.