Determine the domain and range of the inverse function $f ^ { - 1 }$ of the following function $f$
$f ( x ) = - | x + 7 | - 1$, where $x - 7$
A) Domain: $[ - 7 , \infty )$; Range: $[ - 1 , \infty )$
B) Domain: $( - \infty , - 1 ]$; Range: $[ - 7 , \infty )$
C) Domain: $[ - 7 , - 1 ]$; Range: $[ - 7 , \infty )$
D) Domain: $( - \infty , - 7 ]$; Range: $[ 1 , \infty )$
E) Domain: $( - \infty , \infty )$; Range: $( - \infty , \infty )$

Question

Determine the domain and range of the inverse function $f ^ { - 1 }$ of the following function $f$
$f ( x ) = - | x + 7 | - 1$, where $x > - 7$
A) Domain: $[ - 7 , \infty )$; Range: $[ - 1 , \infty )$
B) Domain: $( - \infty , - 1 ]$; Range: $[ - 7 , \infty )$
C) Domain: $[ - 7 , - 1 ]$; Range: $[ - 7 , \infty )$
D) Domain: $( - \infty , - 7 ]$; Range: $[ 1 , \infty )$
E) Domain: $( - \infty , \infty )$; Range: $( - \infty , \infty )$

Quizplus · Accepted Answer

The domain of $f$ is $x > -7$, so the range of $f^{-1}$ is $[ - 7 , \infty )$. $f(x)$ decreases as $x$ increases, with a lower bound of $-1$ (since the absolute value is always non-negative), making the domain of $f^{-1}$ $( - \infty , - 1 ]$.

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

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