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)))
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 ]