Answer:
Option B.
Step-by-step explanation:
Inverse function:
Suppose we have a function y = f(x). To find the inverse function, we exchange x and y on the original function, and then isolate y.
The domain of the inverse function(x values) is the range of the original function(y values).
Original function:
[tex]f(x) = \sqrt{x} - 5[/tex]
Domain is [tex][0,\infty)[/tex], and when [tex]x = 0, f(x) = -5[/tex]. So the range is [tex][-5,\infty][/tex], that is, [tex]y \geq -5[/tex]
Inverse function:
[tex]y = \sqrt{x} - 5[/tex]
Exchanging x and y
[tex]x = \sqrt{y} - 5[/tex]
[tex]\sqrt{y} = x + 5[/tex]
[tex](\sqrt{y})^2 = (x+5)^2[/tex]
[tex]y = (x+5)^2[/tex]
The inverse function is [tex]f^{-1}(x) = (x+5)^2[/tex]
Domain:
Range of the original function is [tex]y \geq -5[/tex], so the domain of the inverse function is [tex]x \geq -5[/tex]. The correct answer is given by option B.
