Answer:
[tex]g\left(x\right)=-\sqrt{x+3}+8[/tex]
Step-by-step explanation:
Given function is [tex]f\left(x\right)=-2\sqrt{x-3}+8[/tex].
Now let's find it's range.
we know that square root function always gives positive output then:
[tex]\sqrt{x-3}\ge0[/tex]
[tex]-2\sqrt{x-3}\le-2\left(0\right)[/tex]
[tex]-2\sqrt{x-3}\le0[/tex]
[tex]-2\sqrt{x-3}+8\le0+8[/tex]
[tex]-2\sqrt{x-3}+8\le 8[/tex]
[tex]f(x) \le 8[/tex]
Hence range of the function is [tex](-\infty,8][/tex].
we can repeat same process to find the range of all the given choices.
we will find that only 3rd choice has same range.
Hence final answer is [tex]g\left(x\right)=-\sqrt{x+3}+8[/tex]
