`f:R to R` is defined as `f(x)= {{:(x^(2)+kx+3",",,"for "xge0),(2kx+3",",,"for "x lt0):}`. If `f(x)` is injective, then find the values of `k`.

Explanation

To determine the values of \( k \) for which the function \( f(x) \) is injective, we need to analyze the function defined as follows:

\[
f(x) =
\begin{cases}
x^2 + kx + 3 & \text{for } x \geq 0 \\
2kx + 3 & \text{for } x < 0
\end{cases}
...