Operations on functions

$\rhd$ 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 $f(h(x))$ .

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