Question 14(b) | BetaMath

Question 14(b)

For what values of the constant $k$ would the function $\displaystyle f(x) = \frac{kx}{1+x^2} + \arctan{x}$ have an inverse?

Solution

To have an inverse, the function needs to be one-to-one. If there are any turning points in the function this is not true. We identify any turning points by taking the derivative and checking for zeros.

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