CPhill

0.03x-0.6=2.4      multiply through by 100 to clear the decimals

3x - 60 = 240     add 60 to both sides

3x = 300    divide both sides by 3

x = 100

65+0.10x=73.40  subtract 65 from both sides

.10x = 8.40     multiply both sides by 100 in order to clear the decimals

10x = 840       divide both sides by 10

x = 84

g (g(-2) )

Go to x = -2 on the graph........look at function g  .....what is it's y value when x = -2??? →  - 1 ....so....

g(-2) = -1 

So ...... g(g(-2)) =  g(-1)      go to x = -1.....look at function g.....

what is its y value when x = -1???? → 1       and that's your answer

f(g(1)) 

Go to x = 1 on the graph.....look at function g.....what is its y value there??   →  5

  So  .....g(1) =  5

So......f(g(1)) = f(5)   now go to x = 5 on the graph....look at function f......what is its y value there???  →   - 6      and that's your answer

64pi = pi*(radius)^2       divide out pi

64  = radius^2   take the positive root of both sides

8 = radius

(2^5*2^-4)^2 *(3^3)^2 *3^-5

(2)^2 * (3)^6 * 3^(-5)  =

4 * 3  =

12

a) y=1/3x +2 and y=3x-6

Here's another way to do this.....we put the second function into the first and evaluate.......if we get "x" back out, we then put the first function into the second and see if we again get "x" returned again......if we get an "x" in both cases, they are inverse functions.....it's easier to do than explain!!!...so we have

The second function put into the first:

(1/3)(3x -6) + 2   =  x - 2  + 2   = x       so far, so good

The first function put into the second:

3[1/3)x + 2] - 6   =   x + 6 - 6  = x

Yep....they're inverses.....the order in which we do this doesn't matter......we could have done the second thing first.......Note......if we don't get an "x" out in the first step, there's no reason to do the second........thet will not be inverses........we have to get an "x" returned in both cases  !!!

Hope this helps.......!!!!!.

I can't make out (a), but here's (b).....

g(f(-2)).......let's look at the f(-2) part, first.....this says  to look for the associated y value where the x value for "f" = -2

So..... we go to x = -2 on the graph  and look at the y value there for the graph of "f"...this is = 1 .......so  f(-2) = 1   ....this makes sense.......(-2, 1)  is a point on "f".......when x = -2, y = 1  ....!!!

And now we have  g(f(-2)) =  g(1)

And now we do the same thing, again.....we look at the graph of g where x = 1 and find the associated y value.....so......when the x value for "g" = 1, the associated y value  = 5

And 5 is your final answer.......!!!

Hope this helps......!!!!

x^14 - x^6    remains just that, unless you want to factor it as :

x^6(x^8 - 1) = x^6(x^4 - 1)(x^4 + 1) =

x^6 (x^2 - 1)(x^2 + 1)(x^4 + 1)  =

x^6 ( x - 1)(x + 1)(x^2 + 1)(x^4 + 1)

It just represents the distance on the number line between a number and 0.......for example.......

l -6 l   = 6 because -6 is 6 units from 0

and

l 4 l  = 4 because 4 is 4 units from 0

Guest could have carried this one step further.....

6sqrt(2) / 7sqrt(2)   =   6 / 7

Also note that    72/98  =  36/49    and the square root of this is just 6 / 7