Chapter 8 Review

On the Friday before break we had the chapter 8 test, which covered sections 8.1-8.8.

Here is a review of the main ideas from this chapter:

8.1- Composition of functions:

-review what a function was

-learned how to handle f(g(x)) and g(f(x))

ex: Let f(x)=2x+4 and g(f)=, find f(g(x)) and g(f(x))

so here u will basically plug and chug, and solve for x

8.2-Inverse of Relations:

- in order to find the inverse of a function, you have to switch where x and y, and solve for x

ex: f(x)=3x -17

f(x) is y

y=3x-17

switch x and y: x=3y-17

solve for y: -now, this is the inverse of the original function, or

-the inverse graph will be reflected over the y=x line

-the domain of a function is the range of the inverse, and the range on the function is the domain of the inverse.

ex: D of f(x)= R of

R of f(x)= D of

8.3- Property of inverse functions:

- Vertical line test- figure if original function is a function on the graph

-Horizontal line test- figure if inverse is a function on the graph

-Inverse function theorem- basically says that if two functions are inverses of each other, it doesn't matter what u plug in, because they will spit out the thing that was plugged.

8.4- Radical notation for the nth roots:

-= , positive nth root of x

-Geometric mean: multiply all the numbers and square root by the number of values.

8.5 products with radicals:

- jail braking method

ex:

27

/\

9 3

/\

3 3

the answer is

8.6 quotients with radicals:

-wfoo- weird form of one

ex: =1, =1

- use wfoo to get rid of radical in the denominator (rationalize the denominator)

ex: multiply by and simplify

8.7 Powers and roots of negative numbers:

-:

-x is positive: n is 2- positive real , n is odd- positive real, n is even- positive real

-x is negative: n is 2- imaginary, n is odd- negative real, n is even - UNDEF

-x is 0: n is 2- 0, n is odd- 0 , n is even - 0

-:

-x is positive: n is 2- all work , n is odd- all work, n is even- all work

-x is negative: n is 2- UNDEF, n is odd- UNDEF, n is even - UNDEF

-x is 0: n is 2- 0, n is odd- 0 , n is even - 0

8.8 solving equations with radicals:

- look out for no solution

-to solve equation with rdical: isolate radical , raise both sides to the nth ALWAYS CHECK SOLUTIONS!

Hope everyone did well, and had a good break!

that's it, 9 more weeks AND WE ARE DONE!