Question

PLEASE AND THANK YOUU, u dont have to draw graph btw

Answer 1

Answer:  sqrt(x+1)+4

This is the same as writing $\sqrt{x+1}+4$

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 $x \ge 4$ and we swapped x and y. This ultimately means $y \ge 4$ and this only occurs if we picked the positive version of the square root (ignoring the negative version).