Mathematics

Mathematics

Problem

Which of the following represents the domain of the function f(x)=7−2xf(x)=\sqrt{7-2x}? a) [3.5,∞)[3.5,\infty) b) (−∞,3.5)(-\infty,3.5) c) (−∞,3.5](-\infty,3.5] d) [0,3.5][0,3.5]
Intuitive explanation

The key to finding a domain is identifying what values of xx make the function defined. Since you can't take the square root of a negative number (in the real numbers), the expression under the radical must be non-negative. Set up an inequality 7−2x≥07-2x \geq 0 and solve for xx to find exactly which inputs are allowed.

Intuitive explanation

The key to finding a domain is identifying what values of xx make the function defined. Since you can't take the square root of a negative number (in the real numbers), the expression under the radical must be non-negative. Set up an inequality 7−2x≥07-2x \geq 0 and solve for xx to find exactly which inputs are allowed.

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