f(x) = x2 + 11x, x ≥ − 11/2

Question

find the inverse

Answer 1

y = x^2+11x
for inverse, switch names and solve for y:

x = y^2+11y
y^2+11y-x = 0
y = (-11±√(121+4x))/2
with the original domain restricted to x >= -11/2, that means

y = -11/2 + √(121+4x)/2

or, consider that
y = x^2+11x
= (x+11/2)^2 - 121/4
restricting the domain to x >= -11/2 means we take just the right branch of the parabola. So, swapping names,

x = (y+11/2)^2 - 121/4
y+11/2 = +√(x + 121/4)
and we get the above result

Answer 2

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