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This is probably really basic math to you guys but I have no idea what to do when I look at it, I tried to find the inverse of x^2 and then plugging it into the g(X) function then finding the inverse of that but I am not sure if that is correct

Find expressions for f inverse and g inverse. For 16 substitute the expression for f inverse into all the x's in g inverse. Then simplify. Also, f inverse is not a function (parabola opening to the right) so you will have to look at the upper and lower branches separately. Let me know if you need more.