QuestionFind a formula for $f^{-1}(x)$. Identify the domain and range of $f^{-1}$. Verify that $f$ and $f^{-1}$ are inverses. $$f(x)=\sqrt{x+5}, x \geq-5$$ $f^{-1}(x)=x^{2}-5$ (Simplify your answer.) Identify the domain of $f^{-1}$. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your A. $D=\{x \mid x \leq\}$ B. $D=\{x \mid \leq x \leq\}$ C. $D=\{x \mid x \neq\}$ D. $D=\{x \mid x \geq 0\}$ E. The domain is all real numbers.
Identify the range of $f^{-1}$. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your ch A. $R=\{y \mid \leq y \leq\}$ B. $R=\{y \mid y \leq \quad\}$ C. $R=\{y \mid y \geq-5\}$ D. $R=\{y \mid y \neq\}$ E. The range is all real numbers.
To verify that $f$ and $f^{-1}$ are inverses, determine $\left(f^{-1} \circ f\right)(x)$ and $\left(f \circ f^{-1}\right)(x)$. $$\left(f \circ f^{-1}\right)(\mathrm{x})=\square \quad\left(\mathrm{f}^{-1} \circ \mathrm{f}\right)(\mathrm{x})=\square$$ (Simplify your answers.)