Answer:
The inverse is [tex]f^{-1}[/tex] (x) = [tex](x+4)^{2}[/tex]
Step-by-step explanation:
(By the way, [tex]f^{-1}[/tex](x) is f negative one of x, like f(x), but inverse)
f(x) = [tex]\sqrt{x}[/tex] - 4 is the same as y = [tex]\sqrt{x}[/tex] - 4
y = [tex]\sqrt{x}[/tex] - 4 start with the equation.
x = [tex]\sqrt{y}[/tex] - 4 switch x and y.
x + 4 = [tex]\sqrt{y}[/tex] add 4 to both sides.
[tex](x+4)^{2}[/tex] = y square both sides.
[tex]f^{-1}[/tex] (x) = [tex](x+4)^{2}[/tex] change y to the inverse f(x) format.
I hope this helps! :)
