D(x)=x^2+2x

Question

C={(x,y)|y=4x-5}
1) D(C(x))

f(x)=1+3 sqrt of x+2
2) f(f(x))

Answer 1

D(x) = x^2+2x
D(C) = C^2+2C
= (4x-5)^2 + 2(4x-5)
= 16x^2 - 32x + 15

f(x) = 1+√(x+2)
f(f) = 1+√(f+2)
= 1+√(1+√(x+2)+2)
= 1+√(3+√(x+2))

Answer 2

D(C(x))
= D(4x-5)
= (4x-5)^2 + 2(4x-5)
expand and simplify if necessary

f(x) = 1 + 3√(x+2)

f(f(x))
= 1 + 3√(x+2)
= 1 + 3√((1 + 3√(x+2))+2)
= 1 + 3√(3 + 3√(x+2) )

testing:
let x = 2
f(2) = 1 + 3√4 = 7
f(7) = 1 + 3√9 = 10

f(f(2)) in my answer
= 1 + 3√(3+3√4)
= 1 + 3√9
= 1+9
= 10

there is a high probability that my answer is correct

Answer 3

I misread the 2nd problem - go with Reiny.