Answer: sqrt(x+1)+4
This is the same as writing [tex]\sqrt{x+1}+4[/tex]
The +4 is not under the square root
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Explanation:
g(x) is the same as y, since they're both outputs of a function
So we have the starting equation y = (x-4)^2 - 1
Swap x and y and solve for y to get the inverse.
y = (x-4)^2 - 1
x = (y-4)^2 - 1
x+1 = (y-4)^2
(y-4)^2 = x+1
y-4 = sqrt(x+1) ... see note below
y = sqrt(x+1)+4
Note: Recall that [tex]x \ge 4[/tex] and we swapped x and y. This ultimately means [tex]y \ge 4[/tex] and this only occurs if we picked the positive version of the square root (ignoring the negative version).
