Question

If f(x)=x^2-1 and g(x)=-2x-3, what is the domain of (fog)(x)?

Answer 1

The domain of (fog)(x) is
`\begin{bmatrix}-8  , -1\end{bmatrix}`

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
`\begin{bmatrix}-8  , -1\end{bmatrix}` Answer