SOLUTION: Given that f(x) = 1 + 4x - x^2 for x ≥ 2. Find the coordinates of the turning point of the function f(x),stating whether it is a maximum or minimum point. Explain why f(x) has an
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-> SOLUTION: Given that f(x) = 1 + 4x - x^2 for x ≥ 2. Find the coordinates of the turning point of the function f(x),stating whether it is a maximum or minimum point. Explain why f(x) has an
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Question 1184854: Given that f(x) = 1 + 4x - x^2 for x ≥ 2. Find the coordinates of the turning point of the function f(x),stating whether it is a maximum or minimum point. Explain why f(x) has an inverse and find an expression for f^-1(x) in terms of x. Answer by robertb(5830) (Show Source):
, and in particular ===> there is a maximum point at x = 2.
(This is to be expected since the coefficient of is negative, and so the parabola opens downward.)
For , f(x) has an inverse function because it is one-to-one over this set. The function is one-to-one because it is strictly decreasing over [2, ).
The inverse function is obtained as follows:
===> ===>
after solving x in terms of y using the quadratic formula. Choose since .
Interchanging the places of x and y, the inverse function is therefore .
