Disclaimer: The material in the videos below comes mainly from outside City Tech. The presentation in these videos may differ from the one given in your class. Please consult with your instructor to confirm whether a particular approach is acceptable in your class.
- $\rhd$ Adding functions (2:32) For $f(x)=9-x^2$ and $g(x) = 5x^2+2x+1$, Sal finds $(f+g)(x).$
- $\rhd$ Subtracting functions (2:16) For $f(x)=2x\sqrt 5-4$ and $g(x) = x^2+2x\sqrt 5-1$, Sal finds $(f-g)(x).$
- $\rhd$ Multiplying functions (2:59) For $f(x)=7x-5$ and $g(x) = x^3+4x$, Sal finds $(fg)(x)$.
- $\rhd$ Dividing functions (6:17) For $f(x)=2x^2+15x-8$ and $g(x) = x^2+10x+16$, Sal finds $\left(\dfrac{f}{g}\right)(x)$.
- $\rhd$ 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 $h(g(f(2)))$.
- * Practice: Type of problem: For $g(x) =\dfrac{3x-5}{x+1}$ and $h(y) = \sqrt{1-3y}$, evaluate $h(g(0))$.
- $\rhd$ Evaluating composite functions (4:09) For $g(x)=x^2+5x-3$ and $g(y)= 3(y-1)^2-5$, Sal finds $(h\circ g)(-6)$.
- $\rhd$ 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 $g(f(x))$.
- * Practice: Type of problem: For $f(x) = x^3-6$ and $h(x) = \sqrt[3]{2x-15}$, find a formula for $f(h(x))$.
