Answer:
[tex]g(x)=-\sqrt{x+3}+8[/tex]
Step-by-step explanation:
we have
[tex]f(x)=-2\sqrt{x-3}+8[/tex]
using a graphing tool
see the attached figure N [tex]1[/tex]
The domain is the interval ------> [3, ∞)
The range is the interval ------> (-∞, 8]
Verify the range of each case by graphing tool
see the attached figure N [tex]2[/tex]
case A) [tex]g(x)=\sqrt{x-3}-8[/tex]
The range is the interval ------> [-8,∞)
case B) [tex]g(x)=\sqrt{x-3}+8[/tex]
The range is the interval ------> [8,∞)
case C) [tex]g(x)=-\sqrt{x+3}+8[/tex]
The range is the interval ------>(-∞, 8] ----> is the solution (same range that f(x))
case D) [tex]g(x)=-\sqrt{x-3}-8[/tex]
The range is the interval ------> (-∞, -8]
