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Chapter 1: Problem 34

Determine the domain of the function represented by the given equation. $$f(x)=\sqrt{4-x}$$

Short Answer

Expert verified
The domain of the function \(f(x) = \sqrt{4-x}\) is \([- \infty, 4]\) inclusive.

Step by step solution

01

Set up the inequality

From the function \(f(x) = \sqrt{4-x}\), it can be seen that the radicand is \(4 - x\). As mentioned above, for the function to be defined in the real number system, the radicand must be greater than or equal to zero, so the inequality to solve is \(4 - x \geq 0\).
02

Solve the inequality

Begin by adding \(x\) to both sides, which gives \(4 \geq x\). This can also be written as \(x \leq 4\).
03

Write the domain

The solution to the inequality \(x \leq 4\) is the interval \([- \infty, 4]\), inclusive. Thus, the domain of \(f(x) = \sqrt{4-x}\) is \([- \infty, 4]\).

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