finding a function????

Question

If g = √(x+2) and F = x+3

what does f equal if f ○ g = F

also for g = 2x and F = cos(x²)

Answer 1

f(√(x+2)) = x+3
Let's let x = 2tan²(y)
So f((√2)sec(y)) = 3 + 2tan²(y)
Now let z = (√2)sec(y) so
(z/√2) = sec(y) so
(z/√2)²-1 = tan²(y)
Thus,
f(z) = 3 + 2((z/√2)²-1) = 1 + z²
f(x) = 1 + x²


f(2x) = cos(x²) so if y=2x
f(y) = cos((y/2)²)
In other words,
f(x) = cos((x/2)²)

Answer 2

First problem.
f(x) = x^2 +1

Second problem.
f(x) = cos(x^2 / 4)