Answer:
The domain of (fog)(x) is [tex]\begin{bmatrix}-8 , -1\end{bmatrix}[/tex]
Step-by-step explanation:
Given function as :
f(x) = x² - 1 And
g(x) = - 2x - 3
So, Function (fog)(x) = ( -2x - 3 )² - 1
Or, (fog)(x) = ( 4x² + 12x + 9) - 1
Or, (fog)(x) = 4x² + 12x + 8
Or, (fog)(x) = 4x² + 4x + 8x + 8
Or, (fog)(x) = 4x ( x + 1 ) + 8 ( x + 1 )
Or, (fog)(x) = ( 4x + 8 ) ( x + 1 )
∴ (fog)(x) lies between - 8 to - 1
Hence The domain of (fog)(x) is [tex]\begin{bmatrix}-8 , -1\end{bmatrix}[/tex] Answer
