Find the Domain y = square root of 8-4x

Problem

y=√(,8−4*x)

Solution

1. Identify the restriction for a square root function. For the output to be a real number, the radicand (the expression inside the square root) must be greater than or equal to zero.

8−4*x≥0

2. Subtract 8 from both sides of the inequality to begin isolating the variable term.

−4*x≥−8

3. Divide both sides by −4 Remember that dividing or multiplying an inequality by a negative number reverses the inequality sign.

x≤(−8)/(−4)

4. Simplify the fraction to find the final constraint on x

x≤2

5. Express the domain in interval notation, representing all real numbers less than or equal to 2.

(−∞,2]

Final Answer

Domain:(−∞,2]

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