+0  
 
0
204
2
avatar

A)B)

Guest Dec 30, 2017
 #1
avatar+90023 
+2

A)  g(x)  =  - x/4  + 4       f(x)  =  4x   +  1/4 

 

So

 

g-1 (x)  

Write y for  g(x)

y  =  -x/4 + 4

y - 4  =  -x/4

4y - 16  =  - x

16 - 4y  =  x        swap  x and y

16  -  4x  =  y   =  g-1(x)

 

f-1(x)

Write y for  f(x)

y  =  4x  + 1/4

y - 1/4  =  4x

[ 4y - 1 ]   / 4   =  4x

[ 4y - 1 ] / 16  =  x         swap  x and y

[ 4x - 1] / 16  =  y  =  f-1(x)

 

(g  o  f  )(x)  =  -  [4x + 1/4] / 4  +  4   =  -x - 1/16 + 64/16   =  63/16  - x

 

(g o f)-1  (x)

Write y  for (g o f)(x)

y  = 63/16 -  x

y - 63/16  = -x

[ 63 - 16y] / 16  =  x    swap  x  and y

[63 - 16x ] / 16  =  y  =  (g o f )-1 (x)

 

 

( f-1 (x)  o   g-1(x)  )   =

 

[ 4  [16 - 4x]  -  1   ]   /  16   =

 

[ 64  -   16x  -  1  ]  /   16  =

 

(63 / 16)  -  x

 

We can conclude that  

 

(g  o  f  )(x)   =   ( f-1 (x)  o   g-1(x)  )

 

 

cool cool cool

CPhill  Dec 30, 2017
edited by CPhill  Dec 30, 2017
 #2
avatar+90023 
+2

B)

Let  f(x)  =  8 * 60  =  480

Let g(x)  =  .20x  +  45

Let h(x)  =  .35x + 20

 

The price  charged by the first company  =   ( g  o  f  )

So we have

.20 (480) +  45  =  $141

 

The price charged by the second company =  (  h   o   f  )

So we have

.35(480) + 20  =   $188

 

The first company is cheaper

 

 

cool cool cool

CPhill  Dec 30, 2017

12 Online Users

avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.