Answer: sqrt(x+1)+4
This is the same as writing
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 and we swapped x and y. This ultimately means
and this only occurs if we picked the positive version of the square root (ignoring the negative version).