Depending on the domain and range, the inverse may or may not be defined.
Assuming it is defined, the inverse function can be derived as follows:
The negative parabola is y = -ax2 + bx + c (where a>0)
so that -ax2 + bx + c - y = 0
using the quadratic formula,
x = [-b ± sqrt(b2 + 4*a*(c-y)]/(-2a)
which is a square root function, and will be real provided that b2 + 4*a*(c-y) > 0
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The inverse of the inverse is the original function, so that the product of the two functions is equivalent to the identity function on the appropriate domain. The domain of a function is the range of the inverse function. The range of a function is the domain of the inverse function.
Standard notation for a quadratic function: y= ax2 + bx + c which forms a parabola, a is positive , minimum value (parabola opens upwards on an x-y graph) a is negative, maximum value (parabola opens downward) See related link.
The original function's RANGE becomes the inverse function's domain.
The inverse of the cubic function is the cube root function.
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