+0  
 
0
211
2
avatar

A)

B)Help would be very much appreciated!

Guest Dec 30, 2017
 #1
avatar+7155 
+1

Question 1

 

a)     f( x )  =  3x2 - 5x + 6    and    g(x)  =  x2 + 3x

 

f o g   =   f( g(x) )

 

f o g   =   f( x2 + 3x )

 

f o g   =    3( x2 + 3x )2 - 5( x2 + 3x ) + 6    I'll let you simplify these if necessary...

 

The domain is (-∞, ∞), and from this graph, we can see that the range is  [47/12, ∞) .

 

g o f   =   g( f(x) )

 

g o f   =  g( 3x2 - 5x + 6 )

 

g o f   =   ( 3x2 - 5x + 6 )2 + 3( 3x2 - 5x + 6 )

 

The domain is  (-∞, ∞), and from this graph, we can see that the range is  [3901/144, ∞) .

 

 

b)     f(x)  =  2x    and    g(x)  =  3 - x

 

f o g   =   f( g(x) )

 

f o g   =   f( 3 - x )

 

f o g   =   23 - x

 

The domain is  (-∞, ∞), and the range is  (0, ∞) .

 

g o f   =   g( f(x) )

 

g o f   =   g( 2x )

 

g o f   =   3 - 2x

 

The domain is  (-∞, ∞), and the range is  (-∞, 3) .

 

 

c)     f(x)  =  sin x    and    g(x)  =  x

 

f o g   =   f( g(x) )

 

f o g   =   f(  x  )             We already know that  f(x)  =  sin x , so....

 

f o g   =   sin x

 

The domain of this is  (-∞, ∞), and the range is  [-1, 1] .

 

g o f   =   g( f(x) )

 

g o f   =   g( sin x )     Plug in  " sin x "  for  " x "  into the function  g(x) .

 

g o f   =   sin x

 

The domain is  (-∞, ∞),  and the range is  [-1, 1] .

hectictar  Dec 30, 2017
edited by hectictar  Dec 30, 2017
 #2
avatar+7155 
+1

Question 2

 

a)    3 - 3x   =   3 - f(x)   =   g( f(x) )   =  g o f

 

b)    x2 - 6x + 6   =   x2 - 6x + 9 - 3   =   (3 - x)2 - 3   =   ( g(x) )2 - 3   =   h( g(x) )   =   h o g

 

c)    6 - x2   =   3 + 3 - x2   =   3 - x2 + 3   =   3 - (x2 - 3)   =   3 - ( h(x) )   =   g( h(x) )   =   g o h

hectictar  Dec 30, 2017

15 Online Users

avatar
avatar
avatar
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.