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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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What is the relationships between inverse functions?
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.
How do you tell if a quadratic function is minimum value or a maximum vale?
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.
If an inverse function undoes the work of the original function the original function's becomes the inverse function's domain?
The original function's RANGE becomes the inverse function's domain.
What is the inverse of a cubic function?
The inverse of the cubic function is the cube root function.
The equation below describes a parabola. If a is negative which way does the parabola open y ax2?
Down
