* Fog:

(fog) (x)= f(g(x)) = √25-(5(x))²

Reemplazando: (fog) (x) = √(25 - (4 + x)²) = (4 + x)² = 16 + 8x + x²

(fog)(x) = √25-(16+5x+2² = √(9 - 8x - x²)

Para que sea real 9 - 8x + x² ≥ 0

x² + 8x - 9 <= 6

(x + 9)(x - 1) <= 0

X pertenecete [-9,1]

b) calcular (fog) (2)

(Fog) es (-2,1] x=2

g(x)=−x+1 x∈ ]−7,7]

f(g(x))=f(-x+1)=-x+1+7

f∘g(x)=-x+8

f∘g(x)=

-x+1 =-4

x-1 =4

x=5

-x+1=9

x-1=-9

x=-8

Dom f∘g= ]−7;5]