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Chapter 2: Problem 23

Find the domain of each function. $$f(x)=\sqrt{24-2 x}$$

Short Answer

Expert verified
The domain of the function \(f(x) = \sqrt{24 - 2x}\) is \(x \leq 12\).

Step by step solution

01

Define the Condition

Any real number under a square root must be greater than or equal to zero. Hence, for the function \(f(x) = \sqrt{24 - 2x}\), the expression \( 24 - 2x \) must be greater than or equal to zero.
02

Solve the Equation

Solve the inequality \(24 - 2x \geq 0\).\nSubtract 24 from both sides to get \(-2x \geq -24\).\nThen, divide by -2 on both sides. However, remember that when you multiply or divide an inequality by a negative number, the direction of the inequality changes, giving you \(x \leq 12 \). So any 'x' less than or equal to 12 falls within the domain.
03

State the Final Domain

The domain of the function \(f(x) = \sqrt{24 - 2x}\) is \(x \leq 12\). This means that 'x' can be any real number less than or equal to 12.

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