Given the function, f(x)=(√x−7)𝑓(𝑥)=(𝑥−7), what is the domain written in interval notation?Question 5Select one:a.[7, ∞)b.x ≤ 7c.x ≥ 7d.(−∞, ∞)e.(7, ∞)

To determine the domain of the function $f(x) = (\sqrt{x} - 7)(x - 7)$, we need to consider the conditions under which the function is defined.

1. Break Down the Problem

• Identify the component expressions within $f(x)$.
• Determine the restrictions imposed by each component on the domain of $f(x)$.

2. Relevant Concepts

• The expression $\sqrt{x}$ is only defined for $x \geq 0$.
• The factor $(x - 7)$ does not impose additional restrictions on the domain beyond this.

3. Analysis and Detail

• For $\sqrt{x}$ to be defined, we require: $x \geq 0$
• Additionally, since a square root must yield a non-negative result, we also need to ensure that $\sqrt{x} - 7$ does not restrict the domain. Setting $\sqrt{x} - 7 = 0$ gives: $\sqrt{x} = 7 \implies x = 49$

Thus, $\sqrt{x} - 7$ is zero at $x = 49$, and it changes sign around this point, but this does not limit the domain further.

4. Verify and Summarize

Combining the constraints, we realize:

• The function is defined for all $x \geq 0$.
• The critical points where the components equal zero or change sign do not alter the domain requirement since they do not result in division by zero or take values that break the function definition.

Final Answer

Thus, the domain of $f(x)$ in interval notation is: $\boxed{[0, \infty)}$

However, based on the given options, none include $[0, \infty)$. The closest representative would likely be option $a: [7, \infty)$, since $\sqrt{x}$ becomes larger than 7 for $x \geq 49$ and does not restrict $f(x)$ in the context given.