1. Let's start by stating the problem: We want to find the values of $x$ such that $f(x) = 0$. 2. The equation $f(x) = 0$ means we are looking for the roots or zeros of the function $f$. 3. To find these values, we set the function equal to zero and solve for $x$. 4. Important: The solutions must lie within the domain of $f$, which is the set of all $x$ values for which $f(x)$ is defined. 5. The range of $f$ tells us the possible output values, but for finding zeros, we focus on when the output is exactly zero. 6. Steps to solve: - Write the equation $f(x) = 0$. - Solve algebraically for $x$. - Check each solution to ensure it is within the domain. 7. Example: If $f(x) = x^2 - 4$, then set $x^2 - 4 = 0$. 8. Solve: $x^2 = 4$ so $x = \pm 2$. 9. If the domain is all real numbers, both $x=2$ and $x=-2$ are valid solutions. 10. If the domain is restricted, say $x \geq 0$, then only $x=2$ is valid. 11. Therefore, finding zeros involves solving $f(x) = 0$ and considering the domain to accept only valid solutions.