Determine the domain and range of the inverse function $f ^ { - 1 }$ of the following function $f$ $f ( x ) = - | x + 8 | - 3$, where $x - 8$
A) Domain: $[ - 8 , \infty )$; Range: $[ - 3 , \infty )$
B) Domain: $( - \infty , - 3 ]$; Range: $[ - 8 , \infty )$
C) Domain: $[ - 8 , - 3 ]$; Range: $[ - 8 , \infty )$
D) Domain: $( - \infty , - 8 ]$; Range: $[ 3 , \infty )$
E) Domain: $( - \infty , \infty )$; Range: $( - \infty , \infty )$

Question

Determine the domain and range of the inverse function $f ^ { - 1 }$ of the following function $f$ $f ( x ) = - | x + 8 | - 3$, where $x > - 8$
A) Domain: $[ - 8 , \infty )$; Range: $[ - 3 , \infty )$
B) Domain: $( - \infty , - 3 ]$; Range: $[ - 8 , \infty )$
C) Domain: $[ - 8 , - 3 ]$; Range: $[ - 8 , \infty )$
D) Domain: $( - \infty , - 8 ]$; Range: $[ 3 , \infty )$
E) Domain: $( - \infty , \infty )$; Range: $( - \infty , \infty )$

Quizplus · Accepted Answer

The domain of $f$ is $x > -8$, which translates to the range of $f^{-1}$ as $[ - 8 , \infty )$. The function $f(x) = - | x + 8 | - 3$ decreases as $x$ increases, starting from $-3$ downwards, making the domain of $f^{-1}$ $( - \infty , - 3 ]$.

Determine the Domain and Range of the Inverse Function f−1f ^ { - 1 }f−1

Determine the Domain and Range of the Inverse Function $f ^ { - 1 }$