Questions: Find the domain of the function. (Enter your answer using interval notation.) g(x) = sqrt(4+x) / (7-x)

Solution Steps

The expression under the square root, $4 + x$, must be non-negative. Therefore: $$4 + x \geq 0$$ $$x \geq -4$$

The denominator, $7 - x$, cannot be zero. Therefore: $$7 - x \neq 0$$ $$x \neq 7$$

The domain of $g(x)$ is all real numbers $x$ such that $x \geq -4$ and $x \neq 7$. In interval notation, this is: $$[-4, 7) \cup (7, \infty)$$

Final Answer