Question

HELP. Assume g^-1(10) is a one to one function. If g(x) = x^2+10x with x greater than or equal to -5, find g^-1 (10).

Answer 1

If we solve the equation\[x = y^{2} + 10y\]for y, we get the inverse of g. Completing the square:\[y^{2} + 10y + 25 = x + 25\]\[y + 5 = \sqrt{x + 25}\]\[y = g^{-1}(x) = -5 + \sqrt{x + 25}\]\[g^{-1}(10) = -5 + \sqrt{35}\approx.916\]