SAT High School

Given that f:x=2x²+8x-10 for the domain x>/=k; find the least value of k for which f is one-one

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Answer 1

The least value of k in which the function f is one to one is k = -∞

What is the least value of k which f is one to one

A function f is considered to be one-to-one if for every unique output y, there is only one unique input x that maps to y. In other words, it means that no two inputs map to the same output.

For the given function f:x=2x²+8x-10, we need to find the value of k for which f is one-to-one for x >= k.

To determine whether the function is one-to-one, we need to check if it passes the horizontal line test. A function is one-to-one if and only if no horizontal line intersects the graph of the function at more than one point.

Since the function is a parabola, its graph opens upwards and therefore it passes the horizontal line test. This means that the function is one-to-one for all values of x, so k can be any real number including negative values.

Hence, the least value of k for which f is one-to-one is k = -∞.

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