consider the function shown. does the function have an inverse that is also a function? use the drop - down…

consider the function shown. does the function have an inverse that is also a function? use the drop - down menus to explain.\n\n$y = \\sqrt{x + 4}, x\\geq - 4$\n\nclick the arrows to choose an answer from each menu.\n\nthe range of the function $y = \\sqrt{x + 4}, x\\geq - 4$ is choose... . for each input of the given domain of $y = \\sqrt{x + 4}$, there choose... of the range. for this reason, the inverse of $y = \\sqrt{x + 4}, x\\geq - 4$ choose... a function.

consider the function shown. does the function have an inverse that is also a function? use the drop - down menus to explain.\n\n$y = \\sqrt{x + 4}, x\\geq - 4$\n\nclick the arrows to choose an answer from each menu.\n\nthe range of the function $y = \\sqrt{x + 4}, x\\geq - 4$ is choose... . for each input of the given domain of $y = \\sqrt{x + 4}$, there choose... of the range. for this reason, the inverse of $y = \\sqrt{x + 4}, x\\geq - 4$ choose... a function.

Answer

Explanation:

Step1: Find the range of the function

For $y = \sqrt{x + 4}$ with $x\geq - 4$, since the square - root function $\sqrt{t}$ where $t=x + 4\geq0$ has non - negative output values, the range of $y=\sqrt{x + 4}$ is $y\geq0$.

Step2: Check the one - to - one property

For each value of $x$ in the domain $x\geq - 4$, there is a unique value of $y$ in the range $y\geq0$. A function has an inverse that is also a function if and only if it is one - to - one. The function $y = \sqrt{x+4},x\geq - 4$ is one - to - one because if $\sqrt{x_1 + 4}=\sqrt{x_2 + 4}$, then $x_1+4=x_2 + 4$ (squaring both sides, since both sides are non - negative), which implies $x_1=x_2$.

Answer:

The range of the function $y=\sqrt{x + 4},x\geq - 4$ is $y\geq0$. For each input of the given domain of $y = \sqrt{x + 4}$, there is a unique value of the range. For this reason, the inverse of $y=\sqrt{x + 4},x\geq - 4$ is a function.