# Determine the inverse for f(x)= 2(x-4)^2+5

justaguide | College Teacher | (Level 2) Distinguished Educator

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A function f(x) and its inverse f^-1(x) are related by: f(f^-1(x)) = x

For f(x) = 2*(x - 4)^2 + 5, the value of f(x) is the same for any x = a and x = -a. As a result it is not possible to determine the inverse function.

A function y = f(x) is a relation where for any value of x, the value of y is unique. The inverse of the given function would be one where each value of x gives 2 possible values of y, this is not permitted for any function.

The function f(x) = 2*(x - 4)^2 + 5 does not have an inverse.
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