Questions: Find the domain of the following function: f(x) = 2 / √(5x + 2)

Solution Steps

The domain of the function is restricted by the expression under the square root, $Bx + C$, since the square root function is only defined for non-negative values. Therefore, the expression $Bx + C$ must be greater than or equal to 0.

Given $Bx + C \geq 0$ and $B \neq 0$, we divide both sides by $B$ to isolate $x$. Since $B$ is positive, the inequality direction remains the same, leading to $x \geq -\frac{C}{B} = -0.4$.

Final Answer