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Using the functions below to produce new functions based upon the description and identify the domain and range of the new functions.

 

f(x)=3x+3

h(x)=e^(2x+1)

i(x)=x^2+4x+3

 

 

    

      1.   r(x)=h(i(x))

 

    

      2.   t(x)=f((h(i(x)))

 Jun 7, 2018
 #1
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f(x)=3x+3

h(x)=e^(2x+1)

i(x)=x^2+4x+3

 

1.   r(x)=h(i(x)).....here. we are putting the function "i"  into the function "h"  

 

r(x)  = e^[(2 (x^2 + 4x + 3) + 1]

r(x)  = e^[2x^2 + 8x + 6 + 1]

r(x)  = e^[2x^2 + 8x + 7]

 

    

 2.   t(x)=f((h(i(x))).......here we are putting the first result into  "f"

 

t(x) = 3(e^[2x^2 + 8x + 7 ] ) + 3  =

t(x) = 3 [ e^(2x^2 + 8x + 7)  + 1 ]

 

 

 

cool cool cool

 Jun 7, 2018

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