The function f: x \(\to \sqrt{4 – 2x}\) is defined on the set of real numbers R. Find the domain of f.
- \(x<2\)
-
\(x \leq 2\)
- \(x = 2\)
- \(x > -2\)
The correct answer is: B
Explanation
\(f : x \to \sqrt{4 -2x}\) defined on the set of real numbers, R, which has range from \((-\infty, \infty)\) but because of the root sign, it is defined from \([0, \infty)\).
This is because the root of numbers only has real number values from 0 and upwards.
\(\sqrt{4-2x} \geq 0 \implies 4-2x \geq 0\)
\(-2x \geq -4; x \leq 2\)