Find the inverse g of (x) = x 2 + 9 with domain x 0 and

Find the inverse g of ƒ(x) = √x² + 9 with domain x ≥ 0 and calculate g'(x) in two ways: using Theorem 2 and by direct calculation.

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THEOREM 2 Derivative of the Inverse Assume that f is differentiable and one-to- one with inverse g(x) = f(x). If b belongs to the domain of g and f'(g(b)) #0, then g'(b) exists and g'(b)= = 1 f'(g(b)) 3